The 16th World Congress of theInternational Federation for the
Promotion of Mechanism andMachine Science
November 5th ~ 10th 2023, Tokyo, Japan

Abstract Booklet

Abstract Booklet of the 16th World Congress of the International Federation
for the Promotion of Mechanism and Machine Science
November 4th 2023
Tokyo, Japan

List of Extended Abstracts
Biomedical Engineering
Yi-Hsuan Lin and Kuei-Yuan Chan
Investigating the Impact of Multiple Tasks on the Estimation of Non-identifiable Muscle
Parameters in Musculoskeletal Models: a preliminary study .................................................. 1
Kaito Yamada, Masanobu Suzuki, Kou Miyaji, Koki Ebina, Kazuya Sase, Teppei Tsujita,
Xiaoshuai Chen, Takashige Abe, Shunsuke Komizunai, Yuji Nakamaru, Taku Senoo, Akihiro
Homma and Atsushi Konno
Development of the Classification System for Surgical Skills in Endoscopic Sinus Surgery................................................................................................................................................. 3
Jacek Bałchanowski, Sławomir Wudarczyk and Artur Handke
Nordic Walking Simulation Research ...................................................................................... 5
Atsushi Takata, Takayoshi Kamada and Yuta Kurashina
Soft Robot for Cell Culture with Multi-directional Mechanical Stretches .............................. 7
Ayumu Nara and Kenji Hashimoto
Power Transmission Mechanism from Upper Limb to Lower Limb by Pneumatic Artificial
Muscles for Development of Self-Assist Suit .......................................................................... 9
Emiko Uchiyama and Wataru Takano
System Stability Evaluation of Head-Shaking Test Using Balance Controller Parameters............................................................................................................................................... 11

Computational Kinematics
Oscar Altuzarra, Monica Urizar, Alfonso Hernández and Enrique Amezua
Parasitic Motions of a Delta Parallel Continuum Robot ........................................................ 13
Vincent Paul Brünjes, Thomas Knobloch, Takahiro Aruga, Mathias Huesing and Burkhard
CorvesDesigning Planar Mechanisms with the Software Mechanism Developer (MechDev) ......... 15i

Amandyk Tuleshov, Recep Halicioglu and Moldir Kuatova
Kinematic Modeling and Analysis of a New Hybrid Seven-Bar Linkage Mechanism............................................................................................................................................... 17
Chedli Bouzgarrou and Khaled Arrouk
3-UCU: a new parallel robot with 6 degrees of freedom ....................................................... 19

Education
Mohan Nagrurkar, P. S. Deole and Prashant Shiwalkar
Survey of Graphic Softwares for teaching Mechanism Synthesis using Path Curvature Theory............................................................................................................................................... 21

Engines and Powertrains
Shanti Mehra, Hardikk Valera, Vikram Kumar and Avinash Kumar Agarwal
Comparative Combustion Characteristics of a Dimethyl Ether (DME) and Diesel FueledEngines .................................................................................................................................. 23

Gearing and Transmissions
Qi-You Zhuang and Shyi-Jeng Tsai
Design and Efficiency Analysis of 3K Paradox Planetary Gear Drives .................................. 25
Quoc-Duy Nguyen and Yu-Ren Wu
Gear tooth topology modification with considering honing wheel dressing in power gear
honing ................................................................................................................................... 27
Javier Sanchez-Espiga, Alfonso Fernandez-del-Rincon, Miguel Iglesias, Ana de-Juan, Pablo
Garcia, Guanghe Huo and Fernando Viadero
Load sharing in planetary transmissions affected by eccentricity and index errors in the sun............................................................................................................................................... 29
Khoe-Qui Le and Yu-Ren Wu
An Analytical Model for Power Skiving Process of Helical Face Gears ............................... 31ii

Yun-Hao Cheng and Yi-Cheng Chen
Designing a Spur Shaper Cutter for a Non-Involute Circular Spline .................................... 33

History of Mechanism and Machine Science
Pierre Larochelle
Ferdinand Freudenstein’s Spatial Kinematics ....................................................................... 35

Linkages and Mechanical Controls
Rui Peng and Gregory Scott Chirikjian
A New Design Method for Thick-panel Origami .................................................................. 37
Lukas Merker, Valter Böhm and Lena Zentner
A tensegrity-based elastic joint element ................................................................................ 39
Alfonso Hernandez, Aitor Muñoyerro, Monica Urizar Arana and Oscar Altuzarra
Coupler curves of a tendon driven hybrid rigid-flexible four-bar. Applications to optimal pathdesign .................................................................................................................................... 41
Yoshihiko Matsumoto and Yasuhiro Inoue
Genetic Algorithm Application in Walking Mechanism Designed with Planar Link
Mechanism ............................................................................................................................ 43

Multibody Dynamics
Marek Wojtyra and Janusz Frączek
Friction-induced redundancy of constraints and its consequences ....................................... 45
Ryogo Mizuno, Satoko Abiko and Teppei Tsujita
A Study on a Method for Maintaining Contact During Capture of Space Debris with an
Magneto-Rheological Damper .............................................................................................. 47iii

Robotics and Mechatronics
Yu-Jen Wang and Shin-Yi Huang
Experimental Determination of Calibrated Accuracy for Six-axis Force and Torque Sensors
Using Compliant Mechanisms .............................................................................................. 49
Pin-Yi Ho, Chia-Hsin Hsieh, Wei-Hsuan Lin, Chih-Wei Li, Cheng-Kuo Sung and Yu-Jen
Chiu
The Effects of Passive Joints on the Stiffness of a Parallel Kinematic Manipulator .............. 51
Gustavo Alfonso Garcia Ricardez, Carl Törnberg, Lotfi El Hafi, Jorge Solis and Tadahiro
Taniguchi
Toward Safe and Efficient Human-Robot Teams: Mixed Reality-based Robot Motion and
Safety Index Visualization ..................................................................................................... 53
Mario Acevedo
An Alternative Solution for Balancing of the 3-PRRR Fully-Isotropic Translational Parallel
Robot ..................................................................................................................................................................... 55
Chung-Jiu Lai and Kuei-Yuan Chan
A Novel Approach to Occupancy Grid Map Merging in Environments with Highly Repetitive
Features ................................................................................................................................. 57
Hao Jian Eugene Tong, Brijesh Patel, Yan-Cen Lin, Zhi-Lin Zhang, Chao-Yi Lin, Chao-Lung
Yang, Ching-Yuan Chang and Po Ting Lin
Human-Robot Collaboration Based on Robot Motion Planning with Adaptive Obstacle
Avoidance .............................................................................................................................. 59
Jorge Solis, Koyu Nakamori, Gustavo Alfonso Garcia Ricardez and Johan Håkansson
Body Gesture Recognition for Collaborative Robots ............................................................. 61
Seito Takeuchi, Shunsuke Komizunai, Taku Senoo and Atsushi Konno
Stem detection using depth camera in red perilla farm ......................................................... 63
Lola Courty and Kenjiro Takemura
Vacuum-powered and fabric-based soft actuator .................................................................. 65iv

Matteo Verotti, Simone Serafino and Pietro Fanghella
Accuracy Criteria for Planar Flexures .................................................................................... 67
Keshab Patra, Arpita Sinha and Anirban Guha
Dynamic Task Capability based Task Allocation for Collaborative Manipulation ................ 69
Jacek Bałchanowski and Sławomir Wudarczyk
Experimental research of a parallel manipulator in a singular configuration ......................... 71
Sangheon Roh, Donghwi Shin, Jeonghyeon Lee, Taegyun Kim and Sungkeun Lee
Design of Underwater Robot system for collecting Floating debris ...................................... 73
Donghwi Shin, Minno Lee, Sangheon Roh and Taegyun Kim
Robust Position Control Through Variable Stiffness and Damping ...................................... 75
Hideto Okura, Shunsuke Komizunai, Taku Senoo and Atsushi Konno
Unfolded Paper Manipulation by a Robot Hand Using High-speed Image Processing ........ 77
Alexander Hoffmann, Patrick Jendro and Andrés Kecskeméthy
Tactile determination of the instantaneous screw axis of a human knee surrogate by a forcecontrolled robot using a Krylov method ................................................................................. 79
Yifan Feng, Yusuke Sugahara, Ming Jiang, Marco Ceccarelli and Yukio Takeda
Design of a hybrid suspended cable and thruster driven parallel robot using hexarotor ....... 81
Yu-Jen Chiu, Wei-Hsuan Lin, Cheng-Kuo Sung and Syanala Jaya Prakash Reddy
Machine Learning Aided Self-Calibration Schemes for Parallel Kinematic Manipulators .... 83
Daigo Tokunaga, Satoshi Nishikawa and Kazuo Kiguchi
Foldable base plate mechanism for parallel link robots .......................................................... 85
Yogesh Pratap Singh and Ashitava GhosalVibration isolation in spacecraft using Gough-Stewart Platform .......................................... 87
Siamak Arbatani, Jozsef Kovecses and Marek Teichmann
Motion Design for Robotic Contact: Insertion Tasks ............................................................ 89v

Łukasz Woliński and Marek Wojtyra
Optimal inverse kinematics solution for redundant manipulators combined with trajectory
scaling ................................................................................................................................... 91
Christian Brans and Andrés Kecskeméthy
Experimental Estimation of Bending of a Cylinder-Piston Actuator of a Parallel Platform byRelative Optical Marker Tracking ......................................................................................... 93
Pramod Pal, Shishir Kolathaya and Ashitava Ghosal
Efficient walking of the quadruped using passive linear spring ............................................. 95Standardization of Terminology
Oscar Altuzarra, Victor Petuya, Mario Acevedo, Miguel Vizcaino and Sebastian Rodriguez
Kinematics of a Tripod Parallel Continuum Robot ................................................................ 97

Transportation Machinery
Xinbo Chen, Jiawei Chen and Wei Wang
A Novel Integrated Driving and Steering Module and Its Multi-objective Optimization ..... 99

Tribology
Youn-Hoo Hwang, Youjin Min and Dae-Eun Kim
Investigation of Tribological Properties of Carbon Coatings Deposited on Polymer Substrate............................................................................................................................................. 101
Luis M. Macareno, Josu Aguirrebeitia, Iker Heras and Martin Eizmendi
Profile optimization in roller bearings for pressure uniformity ............................................ 103
Takayuki Tokoroyama, Chiho Fujiwara and Noritsugu Umehara
The effect of graphite domain direction on the friction coefficient of diamond-like carbon
measured by polarized Raman analysis ................................................................................ 105

vi

Ruixi Zhang, Woo-Young Lee, Noritsugu Umehara, Takayuki Tokoroyama, Motoyuki
Murashima and Yuji Takimoto
The tribological properties of DLC coating with B/Cr codopants and clarification of themechanism at 300oC ........................................................................................................... 107
Yusei Yamada, Motoyuki Murashima, Noritsugu Umehara, Takayuki Tokoroyama and WooYoung Lee
Effect of Fracture Toughness on Wear of DLC Coatings ..................................................... 109
Wenjun Wu, Noritsugu Umehara, Takayuki Tokoroyama, Motoyuki Murashima and Ruixi
Zhang
Development of low-friction DLC surface with liquid film derived from the air using dielectricbarrier discharge .................................................................................................................. 111
Li Lulu, Noritsugu Umehara, Takayuki Tokoroyama and Ruixi Zhang
Tribo-corrosion properties of hard carbonaceous coatings ................................................. 113
Se Jun Shim, Hyeonggeun Jo, Ilkwang Jang and Yong Hoon Jang
Contact behavior of a sliding spherical indenter at supersonic speed .................................. 115
Sung-Jun Lee, Chang-Lae Kim and Dae-Hyeon Kim
Highly Flexible Stretchable Strain Sensor with Sensitivity and Durability for Human-Motion
Detection ............................................................................................................................ 117

vii

Investigating the Impact of Multiple Tasks on
the Estimation of Non-identifiable Muscle
Parameters in Musculoskeletal Models: apreliminary study
Yi-Hsuan Lin and Kuei-Yuan Chan1
Department of Mechanical Engineering,
National Taiwan University, Taipei 10617, Taiwan,chanky@ntu.edu.tw

1

Introduction

Developing subject-specific models that accurately represent the muscle parameters is crucial for improving rehabilitation and sports science outcomes. This
study aims to estimate these parameters using a musculoskeletal (MSK) modeland an optimization technique similar to [1]. However, identifying the correct
parameters can be challenging when multiple combinations of parameters can
produce similar kinematics [2]. To overcome this challenge, we explore the useof optimization tools with multiple performance metrics to determine the parameter values that are non-identifiable. We conduct several simulation cases todemonstrate the effectiveness of our approach.

2

Methodology and Results Discussion

Fig. 1. Flowchart for kinematic trajectory prediction and optimization for N task(s).

In this study, the OpenSim Arm26 MSK model [3] was used to evaluate elbow
joint kinematics and biceps muscle parameters. Tasks were selected for evaluation that involved both load and motion, which the kinematic trajectory fitted
as transformed sine functions. Control signals from the target model and theComputed Muscle Control tool were used to produce target trajectory via the1

Forward Dynamics tool. The difference between the estimated model’s trajectory and the target trajectory was quantified using normalized root-mean-squareerror (NRMSE), with the mean NRMSE used as the objective function in the
optimization problem. The parameters were updated using an optimization technique to find the optimal model’s best-matching trajectory. It is worth notingthat the estimated model differs from the target model solely in terms of theunknown muscle parameters, and the compared trajectories are based on joint
speed. The entire process is illustrated in Fig. 1. The evaluation of parameters using single-task or dual-task was carried out using MATLAB and OpenSim API.
Subsequently, we will explore how optimization tools facilitate the identificationof muscle parameters’ values or the observation of their non-identifiability.
The optimization results for each case and target values are presented in Table 1. The NRMSE for the single-task case was significantly smaller than that of[1], but the difference from the target parameters remained significant. However,when multiple tasks were utilized to evaluate the parameters simultaneously,
the optimal parameters were found to be closer to the target values. Therefore,
utilizing multiple tasks can aid in increasing the accuracy of the estimation.
Table 1. Parameter estimation results for single-task case (#N = 1) / dual-task case(#N = 2) / target values in order, including maximum isometric force (FOM ), tendon
Tslack length (LMO ), and optimal fiber length (LS ). The mean NRMSE for single-task
and dual-task cases are 5.14 × 10−3 and 1.08 × 10−4 , respectively.
FOM (N)LM
LT
Muscle name
O (m)
S (m)
Biceps (long head) 574.49/624.60/624.30 0.1346/0.1156/0.1157 0.2326/0.2724/0.2723
Biceps (short head) 356.98/435.26/435.56 0.1078/0.1321/0.1321 0.1949/0.1923/0.1923

Acknowledgement
This work was supported by the National Science and Technology Council of
Taiwan under grant MOST 111-2223-E-002 -004 -MY3.

References
1. Hinson Jr, Robert, et al. ”Sensitivity analysis guided improvement of anelectromyogram-driven lumped parameter musculoskeletal hand model.” Journalof Biomechanics 141 (2022): 111200.
2. Bujalski, P., J. Martins, and L. Stirling. ”A Monte Carlo analysis of muscle force
estimation sensitivity to muscle-tendon properties using a Hill-based muscle model.”Journal of Biomechanics 79 (2018): 67-77.
3. Delp, Scott L., et al. ”OpenSim: open-source software to create and analyze dynamic
simulations of movement.” IEEE Transactions on Biomedical Engineering 54.11(2007): 1940-1950.

2

Development of the Classification System for
Surgical Skills in Endoscopic Sinus Surgery
Kaito Yamada1 , Masanobu Suzuki2 , Kou Miyaji1 , Koki Ebina1
Kazuya Sase3 , Teppei Tsujita4 , Xiaoshuai Chen5 , Takashige Abe6
Shunsuke Komizunai7 , Yuji Nakamaru2 , Taku Senoo1
Akihiro Homma2 , and Atsushi Konno1
1

1

Grad. school of Information Science and Technology, Hokkaido University, Japan,{yamada@scc, konno@ssi}.ist.hokudai.ac.jp
2
Dept. of Otolaryngology-Head and Neck Surgery, Hokkaido University, Japan
3
Dept. of Mech. Eng. and Intelligent Systems, Tohoku Gakuin University, Japan
4
Dept. of Mech. Eng., National Defense Academy of Japan, Japan
5
Grad. School of Science and Technology, Hirosaki University, Japan
6
Dept. of Urology, Hokkaido University, Japan
7
Faculty of Eng. and Design, Kagawa University, Japan

Introduction

Endoscopic Sinus Surgery (ESS) is an operation that requires a high level ofskill, and there is a need to develop an efficient training method. Therefore,
in this study, the movement data of surgical instruments in ESS and the open
sinus volume as a result of the surgery were obtained through the measurement
experiment. Machine learning was performed using indices calculated from themeasured data. This paper describes the details of the building the classification
model that evaluates the surgical skill of surgeon.

2

Methods

Thirty-six participants performed one full-house ESS for sinus opening using
an elaborate 3D sinus model. Simulated surgeries were measured using a system that can simultaneously measure multiple instruments based on motion
capture (Fig. 1), and several kinematic indices were calculated from the measured data. The volume of the open sinus were also calculated from the CT
images of the postoperative 3D sinus model [1], and these indices were used as
input for building model. The experienced surgeon evaluated the surgical skill
by refereeing endoscopic camera images based on the evaluation index for ESS(ESS-OSATS) [2]. Three machine learning algorithms, SVM (Support Vector
Machine), PCA (Principal Component Analysis based)-SVM, and GBDT (Gradient Boosting Decision Tree), were used in this study. The model accuracy
was evaluate by nested and repeated 10-fold cross-validation. In 10-fold crossvalidation, 36 data sets were divided into 10 data sets, one as test data and nine
as training data. The Friedman test and the Wilcoxon signed-rank sum test were
utilized to compare these accuracies.

3Sinus model

1.0

1.0

0.9

0.9

0.8

0.8

0.7

0.7

0.6
0.5
0.4

p<0.0001

0.3
0.2

Other surgical instruments

Accuracy

Endoscopy

Accuracy

Participant

GBDT

p<0.0001
p<0.0001

SVM PCA-SVM
Methodn.s. No significant

n.s.

0.6

p<0.0001
p<0.0001

0.5
0.4
0.3
0.2

GBDT

SVM PCA-SVM
MethodFig. 1: Overview of ex- (a) Three-class classification (b) Two-class classification
Fig. 2: Accuracy of each classifier
periment

3

Result

The participants were divided into three or two classes according to their ESSOSATS scores. In three-class discrimination, the difference between Experts(n=13, score=65–78) vs. Intermediates (n=9, score=54–64) vs. Novices (n=14,
score=18–53) was examined. In two-class discrimination, the difference between
Experts (n=13, score=65–78) vs. Novices and Intermediates (n=23, score=18–64)
was examined. Figure 2 shows a plot of the classification accuracy after 100 runs
for each method. The validation results showed that the SVM was superior tothe other methods in three-class classification (median accuracy: 59.2%). In thetwo-class classification, SVM and GBDT were superior to the PCA-SVM (79.6%
and 80.0%, respectively). Note that there were no significant difference between
SVM and GBDT.

4

Conclusion

In this study, a surgical skill classification system was developed based on the
kinematic indices and the sinus volume obtained in the measurement experiments using elaborate 3D sinus model. The accuracy of the three classification
methods was compared, and SVM was found to be the best method for the skill
classification system. The next task is to develop a score evaluation system usinga regression method that provides more specific and quantitative feedback.

Acknowledgement
This work was supported by JSPS Grant-in-Aid for Scientific Research (A)(18H04102) & (23H00480).

References
1. K. Yamada, et al.: “A study of techniques for evaluating endoscopic surgery skills,”
SICE SI 2022, pp. 807–810, 2022. (in Japanese)
2. S.Y. Lin, et al.: “Development and Pilot-Testing of a Feasible, Reliable, and Valid
Operative Competency Assessment Tool for Endoscopic Sinus Surgery,” American
Journal of Rhinology & Allergy, vol. 23, no. 3, pp. 354–359, 2009.

4

Nordic Walking Simulation Research
Jacek Bałchanowski1[0000-0002-1510-0122] and Sławomir Wudarczyk1[0000-0003-4953-4516] andArtur Handke1[0000-0002-6727-2751]
1 Wrocław University of Science and Technology, Wrocław, Poland
jacek.balchanowski@pwr.edu.pl,slawomir.wudarczyk@pwr.edu.pl,
artur.handke@pwr.edu.pl

1

Material and methods

The positive health effects of Nordic Walking (NW) have been demonstrated in many
works. However, there is still a lack of evidence regarding how NW walking changes
the stress relief of human limb joints. The study aimed to develop a numerical modelof the human locomotor system during gait and NW and conduct simulation research.
The aim of the simulation was to compare the forces in selected joints during humangait and NW. The first step in building a computer model of human motion was toacquire data from the real object [1]. A measurement system (Fig 1) using inertial IMU
sensors (iSen STT-Systems) was used to obtain the biomechanics of human motion.
NW pole orientation angles and ground forces (along the NW pole axis) were measured
using the developed mobile mechatronic NW measurement system [2, 3]. Both systems
were synchronized in time using an appropriate timestamp (trigger). The measurementsallowed us to obtain the kinematic parameters of individual limb segments. The files
obtained from iSen STT-Systems in BVH format had to be transformed and integrated
with the data obtained from the author's mechatronic NW pole measurement system.
Only adequately prepared data were applied as kinematic excitation in the model.

Fig. 1. Stages of building a model of human biomechanics during gait and with NW poles in
the computer system for dynamic analysis of multibody systems.

The numerical model of human gait biomechanics was based on a structure containing
the upper and lower limbs, the body formed from the combination of the pelvis, thetrunk with the thorax, and the head bedded on the neck. All joints in the model were
replaced with spherical kinematic pairs, thus allowing direct transfer of data obtained

5

from measurements to force relative movements in the model. In joints with fewer degrees of freedom, the corresponding rotations were zero. This approach allowed theformat of the kinematic forcing functions to be unified. The grip of the NW stick withthe hand was also modelled using a spherical joint. Contact between the feet and theground was modelled using flexibility and friction. The developed parametric computermodel made it possible to use measurements of gait parameters obtained for professionals, amateurs of both sexes for simulation studies.

2

ResultAs part of a simulation study of a man during normal gait and NW, the runs of interaction forces in the modelled joints were obtained. Fig. 2 shows example load diagrams
at the left hip and right knee joints during the gait and Nordic Walking of a middleaged man (55 years old, 83 kg body weight, 170 cm high).

Fig. 2. Interaction force runs in the right knee and left hip joint during gait and NW

3Final Remarks

Simulation studies have made it possible to determine and compare loads in selected
human joints during walking with and without NW poles. Analyses of the results of thesimulation studies indicate that proper using NW poles causes less load in some joints
with respect to gait (without NW poles) with similar kinematic parameters of movement.

References
1. Seel T., Raisch J., Schauer T., IMU-based joint angle measurement for gait analysis, Sensors(Basel), 2014, 14.
2. Wudarczyk, S., et al.: Research on the mechatronic gait monitoring system with Nordic
Walking poles. In: 15th International Conference Mechatronic Systems and Materials, MSM
2020, IEEE, cop., Piscataway (2020).
3. Wudarczyk, S., et al.: Experimental research on mechatronic Nordic Walking poles. In: 15th
International Conference Mechatronic Systems and Materials, MSM 2020. IEEE, cop., Piscataway (2020).

6

Soft Robot for Cell Culture with Multi-directional
Mechanical Stretches
Atsushi TAKATA, Takayoshi KAMADA, and Yuta KURASHINA
Department of Mechanical Systems Engineering,Tokyo University of Agriculture and Technology, Japan, takata-a@go.tuat.ac.jp

Keywords: Soft robot, Cell culture, Pneumatic actuator.

1

Introduction

To date, the mechanism of how skeletal muscle matures is unproven. Thus, some diseases such as muscular dystrophy are still intractable. One of the key factors in myoblasts’ maturation that researchers have been tackling is mechanical stimuli. In a previous study, the myoblasts of the mouse were repeatedly stretched in one direction using a novel flexible cell chamber, and its real-time response was observed during incubation [1]. However, real mechanical stretches of myoblasts in our body are multi-directional because muscles not only contract but also are bent. Therefore, in our study,a soft robot actuated by pneumatic power is utilized to load multi-directional strain on
cells. Although some bioengineering studies utilized soft robots that move a single
bending-like motion [2], our robotic chamber is the first case of multi-directional movement. After that, deformations were measured by image processing.
Cell Chamber

(a)

2ch

(b)

y

Pneumatic
hose

x
1ch

Pouch motor

3ch

PillarFig. 1. Soft robotic chamber moves in multi-direction.
(a) Overview of the robot. (b) Deformation was captured by a microscope.

2

Design of Robot with Pneumatic Actuator

The developed system is shown in Fig. 1(a). The cell chamber was made by casting
PDMS. The pouch motor [3] is an actuator that is made of heat-sealed nylon film. The
light brown exoskeleton parts were PEEK. Since all parts can be sterilized, this system7

is suitable for cell culture. As shown in Fig. 1(b), three pouch motors 1ch, 2ch, and 3ch
contract when air pressure is applied through the air hoses. And they pull the chamber
in a horizontal xy-plane. Furthermore, Fig. 2 shows C2C12 cells that were suspended
in collagen gel and seeded on the culturing zone.

3

Evaluation of Strain using Image Processing

The strain generated in the chamber by pouch motors was captured from the top using
a microscope. There are three pillars in the culturing zone, and we measured the deformation of a triangle with them as vertices. An air pressure of 60 kPa was applied to 1ch,
2ch, and 3ch in turn. The strain assumed that the deformation is linear in the same way
as the triangular elements in FEM method. Figure 3 shows the resultant x-strain 𝜀𝑥 , ystrain 𝜀𝑦 , and xy-shear strain 𝛾𝑥𝑦 . A maximum strain of 7.1% occurred. The strain ofour device needs to be enlarged because muscle cells in vivo contract by about 10%.

Fig. 2. Cells in developed chamber.

4

Fig. 3. Air Pressure 60 kPa caused up to 7.1% strain.

Conclusion

In this paper, we developed a cell chamber with soft actuators that give multi-directional stretch. The strain generated in the culturing zone was measured by image processing, and the strain was up to 7.1%. In the future, we will work on improving theactuator for larger strain and cell culture with stretching stimuli.

References
1. K. Kasahara, Y. Kurashina, S. Miura, S. Miyata and H. Onoe, “Real-Time Three- Dimensional Single-Cell-Resolution Monitoring System for Observation of Dynamic Cell Behavior under Mechanical Stimuli,” 2021 IEEE MEMS, 454-457(2021).
2. Paek, J., Song, J.W., Ban, E. et al. Soft robotic constrictor for in vitro modeling of dynamic
tissue compression. Sci Rep 11, 16478 (2021).
3. R. Niiyama, D. Rus and S. Kim, “Pouch Motors: Printable/inflatable soft actuators for robotics,” 2014 ICRA, 6332-6337(2014).

8

Power Transmission Mechanism from Upper Limb to
Lower Limb by Pneumatic Artificial Muscles forDevelopment of Self-Assist Suit
Ayumu Nara1 and Kenji Hashimoto2[0000-0003-2300-6766]
1 Meiji University, 1-1-1 Higashi-Mita, Tama-ku, Kawasaki, Kanagawa 214-8571, Japan

2 Waseda University, 2-7

Hibikino, Wakamatsu-ku, Kitakyushu, Fukuoka 808-0135, Japankenji.hashimoto@waseda.jp

Walking is necessary to maintain quality of life. In recent years, the percentage of
people who run to keep their health has increased, but running places a heavy load on
the lower body, making it difficult for people whose muscles have begun to deteriorate to run long distances. This is why people of all ages are attracted to Nordic walking (walking with poles), which actively uses the upper body [1]. Similarly, if theenergy of the upper body can be transferred to the lower body, the load on the lower
body can be reduced. Therefore, our long-term goal is to develop a support suit that
can transfer the energy of a runner’s upper body to the lower body so that people whohave begun to lose muscle can still enjoy jogging and running.
There are many walking support robots with electric actuators, such as Robot Suit
HAL® [2]. However, most of them support walking with the actuators installed in thewalking support robot, so they have little effect on increasing the wearer’s muscle
strength. Therefore, our goal is to develop a “self-assist suit” that can assist the wearer
by its own power in the long term. The objective of this research is to develop a power transmission mechanism that can transfer energy from the upper limb to the lower
limb for the realization of the self-assist suit.
There are various possible methods of transmitting power from the upper limb to
the lower limb, including the use of link mechanisms, wires, and rubber. In this study,
we chose to use air pressure to transmit power, with the possibility of future expansion, such as transmitting power from one joint of the upper limb to multiple joints of
the lower limb. Specifically, McKibben artificial muscles are used in the powertransmission mechanism. Two pressurized artificial muscles are connected in series,
and when one artificial muscle (the drive side) is extended, the other (the driven side)
contracts (see Fig. 1 (a)).
Focusing on the knee joint during walking, the angular change is approximately 60
degrees [3]. Considering the thickness of the human thigh and lower leg, the required
contraction rate for artificial muscles is about 10%.
The McKibben artificial muscles consist of a rubber tube covered with a synthetic
fiber sleeve. When pressure is applied to the rubber tube, the radial expansion force ofthe rubber tube is converted into an axial contraction force by the synthetic fiber
sleeve. Due to the working principle, the contraction rate of McKibben artificial muscles varies depending on the combination of material and dimensions of the rubber
tube and sleeve.

9The urethane tube is often used for the rubber tube in the McKibben artificial muscle, but as shown in Fig. 1 (b), this did not provide sufficient contraction. As a resultof trial and error, we used R-Air (a racing bicycle tube sold by Panaracer Co., Ltd.),
which has excellent elasticity, for the rubber tube. When the artificial muscle using RAir on the drive side was pulled under 0.05 MPa pressure as the initial condition, acontraction rate of more than 10% was obtained. Furthermore, when the volume ofthe drive-side artificial muscle was relatively increased by making the natural lengthof the driven-side artificial muscle 1/2 the length of the drive-side artificial muscle, aneven greater contraction rate was obtained, as shown in Fig. 1 (b).
Through experiments, it was suggested that a power transmission mechanism using
pneumatic artificial muscles with R-air could be applied to a self-assist suit. Fig. 1 (c)shows the self-assist suit currently under development using the power transmission
mechanism described in this study.
Filter / Regulator

ControlvalvesArtificial
muscles
Artificial muscle(drive side)

Contraction rate %

(a)

18
16
14
12
10
8
6
4
2
0

: Urethane tube (300 mm length): R-Air (300 mm length): R-Air (150 mm length)

Artificial muscle(driven side)

0

200

400

Tensile force N

(b)

600

800

Front

Back

(c)

Fig. 1. Proposed power transmission mechanism: (a) Pneumatic schematic of power transmission mechanism using pneumatic artificial muscles, (b) Experimental results of power transmission mechanism evaluation, (c) Self-assist suit using the power transmission mechanism.

References
1. Tschentscher, M. Niederseer, D., Niebauer, J.: Health Benefits of Nordic Walking: A Systematic Review. American Journal of Preventive Medicine 44(1), 76-84 (2013).
2. Sankai, Y.: Leading Edge of Cybernics: Robot Suit HAL. In: 2006 SICE-ICASE International Joint Conference, pp. P-1-P-2, Busan, Korea (2006).
3. Perry, J.: Gait Analysis: Normal and Pathological Function. Slack Inc. (1992).

10

System Stability Evaluation of Head-Shaking
Test Using Balance Controller Parameters
Emiko Uchiyama1 and Wataru Takano2
1

The University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan,
e-uchiyama@g.ecc.u-tokyo.ac.jp,
home page: http://www.euchiyama.jp
2
Osaka University, 1-3, Machikaneyama-cho, Toyonaka-shi, Osaka, 560-8531, Japan,

1

Background

Fall and consequent fractures make elderly frailty and lead them to use a nursing
cares. Robinovitch[1] found that elderly people in care facilities fall by theirincorrect shifts of center of motions. On the other hand, falls in homes are not wellsurveyed due to diﬃculties of studying as keeping their privacy. Our group has
conducted interview research to the elderly who had experienced hip fractures
after their falls, and pointed out that repetitive turns during going from/to toilet
may be a trigger of losing balance and one of causes of falls[2]. From this pointof view, adequate means to keep the home environments safe even if they once
have experienced fall and fracture is required. Ueda[3] proposes the intervention
ways to notice the patients of their fall risk when people discharged using theirroom plan. In this research, we aimed at proposing a risk estimation methodthat evaluates the elderly peoples’ fall risk at their homes from motions fromthe view of the system stability. As the ﬁrst step, we consider static standings
and discuss its stability.

2

Related work and Method

We hypothesized that the elderly people’s stability controls to unexpected disturbances turn to be unstable as they repeat turns (in other words, shake theirheads). For the balance control in a stationary state we have already proposed atest to identify people’s internal balance control parameters[4]. In this research,
we ﬁrst identify the control parameters in static state and examine stability andresponsiveness of the system using the identiﬁed parameters.

3

Experiment and Result

We measured participants’ joint positions and ZMP positions during motions
using a motion capture system. The parameters of the controller was identiﬁed
referring the proposed method in [4]. CoM/ZMP trajectories during test wereanalyzed. Also, median value of the CoM trajectory as the point to which the11data converge in the control system and responsiveness to the impulse input of
the system using the identiﬁed parameters was analyzed. One set of examples ofanalysis is shown on Fig. 1.

(A) CoM and ZMP trajectorywith footprint(B) CoM trajectory(Left: x-direction,
Right: y-direction)(C) Responsivenessof the system

Fig. 1. The CoM trajectory and responsiveness of the controller was analyzed.

4

Conclusion

We proposed the scheme that evaluates the balance abilities of people as usingparameters of the controller. To discuss the stability before and after the balance screening test, the responsiveness and the convergence of the CoM position
after disturbances were analyzed. Since we only considers the static state at thecurrent method, expanding this theory to the dynamic motions is the next step.

Acknowledgement
This research is supported by SECOM Science and Technology Foundation and KAKENHI(20K19858).

References
1. S.N.Robinovitch, F. Feldman, R. Schonnop Y. Yang, P.M. Lueng, T. Sarraf, J. SimsGould, and M. Loughin. Video capture of the circumstances of falls in elderly people
residing in long-term care: an observational study. The Lancet, Vol. 381, pp. 47–54,
2013.
2. BK.Son, M. Akishita, E. Uchiyama, S. Imaeda, S. Taniguchi, Y. Sumikawa, S. Unyaporn, T. Matsubara, S. Tanaka, T. Tanaka, T. Otsuki, J. Okata, and K. Iijima.
Multiple turns: Potential risk factor for falls on the way to the toilet. Geriatrics &Gerontology International, Vol. 19, pp. 1293–1295, 2019.
3. T. Ueda, Y. Higuchi, G. Hattori, H. Nomura, G. Yamanaka, A. Hosaka, M. Sakuma,
T. Fukuda, T. Fukumoto, and T. Nemoto. Eﬀectiveness of a tailored fall-prevention
program for discharged older patients: A multicenter, preliminary, randomized controlled trial. International Journal of Environmental Research and Public Health,Vol. 19, No. 3, 2022.
4. E. Uchiyama, W. Takano, Y. Nakamura, T. Tanaka, and K. Iijima. Head shaking
test: Human balance ability evaluation test by estimating control parameters for fall
preventions. The 6th Jc-IFToMM International Symposium, 2023(to be published).

12

Parasitic Motions of a Delta Parallel Continuum
Robot
Oscar Altuzarra, Mónica Urizar, Alfonso Hernández, and Enrique Amezua
University of the Basque Country UPV/EHU,
Torres Quevedo s/n, Bilbao 48013, Spain
Contact author: monica.urizar@ehu.eus

One of the most successful designs of a Lower Mobility Parallel mechanisms
is the family of translational parallel mechanisms called Delta. The articulatedparallelogram used in each limb introduces a constraint on the rotation of theend-effector about the normal to the parallelogram’s plane, generating a coupled
restriction of the three possible rotations, i.e. a pure translational motion of theend-effector. One side of the parallelogram is attached to the end-effector while
the other one is translated with an actuator of different types, configuring thevertical or horizontal Delta, Keops-Delta and rotational Delta.

Fig. 1. Flexible Keops-Delta 3P F F SS with Cosserat Rods

In order to design a flexible alternative to those translational mechanisms wehave to bear in mind that hard geometric constraints are not possible in suchflexible devices. By introducing flexible parallelograms, as shown in Fig. 1, themotion of the end-effector is not fully restricted to avoid rotations due to theflexibility of the rods. The aim of this contribution is to show the design process
to get a quasi-translational behaviour of the system over a certain workspace
under a certain range of loads by selecting appropriate dimensions of the system.
The 3P F F SS Delta is a coupled mechanism of flexible rods, the rigid endeffector being connected to 3 parallelograms formed by flexible rods, which are13attached to the end-effector by spherical joints at their distal-ends Bi while theproximal-ends Ai are clamped to a rigid segment, with clamping orientation to
be kept in vertical direction. These proximal segments are directly translated byactuators, in the Keops-Delta of Fig. 1 being placed on a pyramidal scheme.
The FK consists of determining the pose of the end-effector, i.e pP and thequaternion ẽ, when input values for each rod ρi and a load are imposed [1]. Guessvalues are required to start a boundary value problem on a vector of 25 geometric and static equilibrium residuals. A Newton method is used in the shooting
method, requiring the evaluation of a Jacobian of the residue vector with respect to the problem’s variables. After each iteration, guess values are updated
and the process starts again until residuals’ values are below a specified tolerance. In Lower Mobility Parallel Continuum Mechanisms, output components
are obtained without any distinction on whether they are principal or parasitic.
However, for the IK it is essential to assess appropriately which components are
the principal ones. We will show that some translational and rotational ellipsoids can be found to achieve this target. Then, these output components are
imposed in the IK while the parasitic ones are unknowns. Once these Kinematic
problems are solved, a workspace and singularity analysis [2] can be performed.
Experimental validation is performed on a prototype of the Keops-Delta. An
actuators’ platform was designed with 3 linear guides controlled by stepper motors. A system was developed for the electronic control, which includes a MATLAB GUI application that communicates through a serial port with a microcontroller, allowing the control implementing FK and IK solutions. For measuring
the parasitic rotational outputs, the MMA8451Q three-axis accelerometer sensor
is used. This sensor can detect accelerations on the x, y, and z axes and has adigital sensitivity of 4096 counts per g. The data is collected at 14-bit resolution,and the analog output is converted to digital information using an ADC before
being analysed by a microcontroller. This analysis aids in the determination ofan object’s orientation using a straightforward trigonometric algorithm.

Acknowledgments
The authors wish to acknowledge the financial support received from the Spanish
Government through the Ministerio de Ciencia e Innovación (Project PID2020116176GB-I00) financed by MCIN/AEI/10.13039/501100011033 and the support for the research group through Project IT1480-22 provided by the Departamento de Educación from the Regional Basque Government.

References
1. Black, C.B.; Till, J. and Rucker, D.C.: Parallel Continuum Robots: Modeling, Analysis, and Actuation-Based Force Sensing. IEEE Transactions on Robotics. 34, 29-47(2018) 10.1109/TRO.2017.2753829
2. Briot,S. and Goldsztejn, A.: Singularity Conditions for Continuum Parallel Robots.
IEEE Transactions on Robotics. 38, 507-525 (2022) 10.1109/TRO.2021.3076830

14

Designing Planar Mechanisms with the Software
Mechanism Developer (MechDev)
Vincent Brünjes1, Thomas Knobloch1, Takahiro Aruga2, Mathias Hüsing1, Burkhard
Corves1
1 Institute of Mechanism Theory, Machine Dynamics and Robotics, RWTH Aachen University,

Eilfschornsteinstraße 18, 52062 Aachen, Germany

2 Iwatsuki Lab., Tokyo Institute of Technology, Room #351, Ishikawadai-1 Building

2-12-1, Ookayama, Meguro-ku, 152-8550 Tokyo, Japanhuesing@igmr.rwth-aachen.de1

Extended Abstract

The Institute of Mechanism Theory, Machine Dynamics, and Robotics (IGMR) at
RWTH Aachen University is currently developing the software "Mechanism Developer" (MechDev) for the analysis and synthesis of planar mechanisms with one ormore degrees of freedom. The focus of the development is to create a powerful toolfor engineers that distinguishes itself from existing software solutions not only by its
performance but also by its intuitive operation. As a goal, the software should bemade accessible also to those who do not have a background in mechanism theory.
At the IGMR different contributions have already been made towards the kinematic calculation of planar linkages [2; 6], the synthesis and analysis of cam mechanisms[1; 3; 4], and the analysis of gear mechanisms [5]. This contribution focuses on theusage of the software to these ends. For this purpose, the current range of functions of
MechDev is first summarized. Subsequently, these functions are validated with an
example mechanism.
The current scope of functions includes the kinematic analysis of planar linkages
consisting of revolute and prismatic joints, cam followers, as well as the kinetostatic
analysis for the calculation of drive torques induced by gravitational force, external
forces, and spring-damper elements. Joint friction can also be considered. In addition,
MechDev offers the function to synthesize cam wheels by specifying the desired output motions or analyze cam mechanisms based on imported cam geometries. The
specification of such output motion, which provides the basis for cam wheel synthesis, can also be used for the motion design of servo motors. Furthermore, both thedevelopment and analysis of gear and gear-coupler mechanisms is possible.
The functions mentioned before, as well as further features, are presented using
the cutting mechanism included in [7] as an example. A screenshot using the software15

is shown in Fig. 1 (a). Given the available methods of interaction with MechDev(shown in Fig. 1 (b)) it is possible to optimize the mechanism interactively by dragand-drop. The presentation shows the complete design process, from the definition of
the mechanism in MechDev to the interactive optimization of the drive torque.

(a)

(b)

Fig. 1. A cutting mechanism from VDI 2142-3 [7] (a) and a screenshot from MechDev (b).

References
1. Beckermann, A.; Müller, M.; Hüsing, M.; Corves, B., Analytical Kinematic Analysis of
Cam Mechanisms in MechDev, In: Uhl, T. (Ed.), Advances in mechanism and machinescience, Cham, Switzerland: Springer Nature Switzerland AG, 2019, ISBN 978-3-03020130-2, S. 429–438.
2. Corves, B.; Huesing, M.; Müller, M., A Model-View-Controller based Software Approachfor the Interactive Design of Planar Mechanisms, In: Zhang, X.; Wang, N.; Huang, Y.
(Ed.), IFToMM Asian Mechanism and Machine Science, Bengaluru, India, 2018.
3. Corves, B.; Huesing, M.; Müller, M.; Beckermann, A., Analyse von Kurvengetrieben in
MechDev, In: Gössner, S. (Ed.), Tagungsband 13. Kolloquium Getriebetechnik, Fachhochschule Dortmund, 18. - 20. September 2019, Berlin: Logos Berlin, 2018, ISBN383254979X.
4. Müller, M.; Hüsing, M.; Beckermann, A.; Corves, B., Linkage and Cam Design with
Mechanism Developer (MechDev), In: 25th Jc-IFToMM Symposium, Kanagawa, Japan,
2019.
5. Knobloch, T.; Brünjes, V.; Hüsing, M.; Corves, B., Analyse von Koppel-, Kurven-, Räderund Räderkoppelgetrieben mit Mechanism Developer (MechDev), In: Berger, M., Corves,
B., Lüth, T. (Ed.), Tagungsband Getriebetagung 2022, Technische Universität Chemnitz,
22. - 23. September 2022, Berlin: Logos Berlin, 2022, ISBN 978-3-8325-5552-8.
6. Müller, M.; Mannheim, T.-P.; Hüsing, M.; Corves, B., MechDev – A new Software forDeveloping Planar Mechanisms, In: Kecskeméthy, A. et al. (Ed.), Third Conference on Interdisciplinary Applications in Kinematics, Lima, Peru, 2018, ISBN 978-3-030-16422-5,
S. 151–158.
7. VDI 2142, Auslegung ebener Kurvengetriebe - Praxisbeispiele, Norm, Verein Deutscher
Ingenieure, Berlin: Beuth Verlag GmbH, 2013.

16

Kinematic Modeling and Analysis of a New
Hybrid Seven-Bar Linkage Mechanism
Amandyk Tuleshov1 , Recep Halicioglu1,2 , and Moldir Kuatova1
1

1

U.Joldasbekov Institute of Mechanics and Engineering, Almaty, Kazakhstan
2
Turkish Machine Theory Association, Turkey

IntroductionMore than 50% of forming materials processes in the engineering industry arecarried out using forging machines, including crank presses, due to some advantages such as high productivity, the possibility of various types of stamping, andhigh precision stamping in the extreme position of the working body. One of
the most essential directions in developing crank presses is their multi-link linkages. Using multi-link mechanisms is a reasonably effective way to implement
the requirements of stamping technology. In addition, most interest has been focused on their driving systems. Because hybrid mechanisms are driven by both aconstant-speed and servo motor, some problems are experienced, and it is necessary to solve these problems. This study aims to present a new hybrid seven-bar
linkage mechanism with related kinematics modeling and analysis. The mechanisms’ kinematics is studied with inverse problem. This mechanism provides
flexible motion by using a servo motor with a lower power capacity. In addition,
the linkage flexibility is achieved using a rocker pair that provides programmablemotion output.

2

Kinematic modeling and analysis

2.1

Mechanism configuration

A hybrid seven-bar linkage mechanism is presented
in Figure 1. The mechanism is composed of: crank(r), links (l, d), slider (D), and coulisse mechanism(C(xc , yc )). All joints are revolute. The crank andcoulisse mechanism are driven by a constant speed
motor (CSM) and a servo motor (SM). In the Bottom dead center point (BDC) of the slider, r and l are
lined up at one angle, and d and slider are lined up ina straight line. The TDC is the top dead center point. Fig. 1. Schematic illustraThe coulisse is a mechanical linkage that facilitates tion of a new hybrid seventhe conversion of a rocking or rotational motion into bar linkage mechanism
a reciprocating motion and vice versa. The main advantage of the coulisse mechanism is that it provides

17

a reasonably high speed of slider reverse stroke. In addition, the coulisse mechanism can transmit much less effort than the crank mechanism. The coulisse
mechanism is connected with the slider through an adjusting link BC (p) totune its motion. S1 is the slider displacement.
2.2

Kinematic analysis

In this section, the inverse kinematics equations of a 2DOF hybrid mechanismwith a seven-bar configuration are obtained (Figure 1). Two loop closure equations are considered and written in vector form. By resolving them into x andy components and differentiating, can be obtained the p representing the servo
motor’s linear displacement, velocity, and acceleration. In inverse kinematics
analysis, the input values are ϕ and S1 variables, and θ, µ, ϕ, ϑ = f(ϕ, S1 ).
p(1)p = ± (xc − r cos(ϕ) − l cos(θ))2 + (yc − r sin(ϕ) − l sin(θ))2ṗ = rϕ̇ sin(ϕ − µ) + lθ̇ sin(θ − µ)(2)p̈ = pµ̇2 + rϕ̈ sin(ϕ − µ) + rϕ̇2 cos(ϕ − µ) + lθ̈ sin(θ − µ) + lθ̇2 cos(θ − µ) (3)3Motion Applications

The angular velocity of CSM is a constant value (positive direction 1, 256rad/sec).
The slider stroke is 30 mm. The designed dwell motion with kinematic specifications is obtained. By providing inverse kinematics analysis, we received thekinematics characteristics of SM.

4

Kinematic Modeling

The proposed hybrid mechanism model was developed by solving motion equations in MATLAB.

5

Conclusion

In this study, a new hybrid seven-bar linkage mechanism was presented withrelated kinematics modeling and analysis. It is studied with inverse problem
This proposed mechanism configuration provides flexible motion and lower power
capacity by using a servo motor. The linkage flexibility is achieved using a rocker
pair that provides programmable motion output. In this way, different motion
scenarios can be implemented.

6

Acknowledgment

This research was supported by the Funding of the Kazakhstan Ministry of
Science and Higher Education (Project No. AP19577094). We also would liketo sincerely thank the Joldasbekov Institute of Mechanics and Engineering forproviding resources.

18

3-UCU: a new parallel robot with 6 degrees of freedom
Chedli Bouzgarrou1 and Khaled Assad Arrouk2
1 Université Clermont Auvergne, CNRS, Clermont Auvergne INP,
Institut Pascal, Department M3G, 63000 Clermont-Ferrand, France
chedli.bouzgarrou@sigma-clermont.fr
2 Al-Baath University, The Faculty of Mechanical and Electrical Engineering,
Department of Mechanical Design and Production, Homs, Syria
kharrouk@albaath-univ.edu.sy

Keywords: mechanism synthesis, linear – angular transmission, parallel robots,decoupled motions.

1

Introduction

Parallel kinematics Machines (PKMs) or robots have been widely studied during thepast three decades. The majority of known PKMs have only one actuated joint for eachlimb, preferably a joint close to the fixed base. In contrast, robots with more than one
actuated joint per limb have attracted less interest. This is mainly due to the loose ofsome benefits of PKMs such as mobile mass reduction. In this paper, we introduce atransmission device that enables the full actuation of the two degrees of freedom(DOFs), translation and rotation, of the equivalent of a cylindrical joint [1]. Such atechnology makes possible the actuation of two DOFs of a manipulator limb in a compact an efficient way. Thus, new generic mechanism architectures can rise based on
fully actuated cylindrical joints such as the 3-CRS manipulator [2]. Another interesting
robot architecture is the 3-UCU that we present for the first time in this paper, withpartially decoupled motions.

2

Linear – angular transmission

We propose a linear – angular transmission devise described by the kinematic diagramof Fig. 1a. This devise uses as inputs 2 screws (1a) and (1b), with parallel axes, connect
to the support (0) by two revolute joints. Two nuts (2a) and (2b) are mounted on eachof these screws and each of them is connected by a revolute joint to the carriage (3).
The axes of the revolute joints between the carriage (3) and the nuts (2a) and (2b) are
parallel to the axes of the screws. The carriage (3) is connected by a prismatic joint tothe support (0) along an axis parallel to those of the screws. An output shaft (4), isconnected by a revolute joint to the carriage (3) whose axis is also parallel to that of thescrews. Each nut is connected to the output shaft (4) by a transmission element such asa belt (5a and 5b), a chain or a gear train, so as the angular speed of the nuts (2a or 2b)
and that of the output shaft (4), with respect to the carriage (3), are proportional. Sucha design allows translation and a rotation, of parallel axes, of the output shaft (4) with19

respect to the support (0). Therefore, the connection between the output shaft (4) andthe support (0) is then equivalent to a motorized cylindrical joint. Fig. 1b gives an illustration of the mechanical design of the proposed device, with gear transmissions,
integrated in a robot limb. The transmission is symmetric and generates independent
output translation and rotation.

3

3-UCU design

If we use the transmission device presented above within a limb of a parallel mechanism, we have two actuated DOFs in this limb. In order to synthetize parallel robot
architecture with such a device, we can use Gogu’s mobility formulae [3] to determine
the possible remaining joint types and their arrangements to obtained the required DOFsof the limb. Therefore, to have a PKM with 6 DOMs and 3 limbs, we need 6 DOFs perlimb. One of possible solutions is to add two universal joints as we propose for the 3UCU parallel robot depicted in Fig. 1c. Moreover, in order to achieve motion decoupling between translation and rotation, the three U-joints connecting the limbs to themobile platform must have all their axes concurrent at one point, the center of the mobile platform (MPF). Therefore, only translational motorized joint variables control the
position of the MPF. For a given position of the MPF, only rotational motorized joint
variables control the orientation of the MPF such as a spherical robot. In addition, theproposed design reduces bending loading since each isolated limb is attached to the restof the mechanism by U-joints at both ends.

(a)

(b)

(c)

Fig. 1. Linear – angular transmission device (a), CAD model of the transmission device integrated in 3-UCU limb, (c) CAD model of the 3-UCU robot.

References
1. Bouzgarrou, C.: Mechanical transmission device and system comprising such a device. Patent EP3507524, (2019).
2. Bouzgarrou, C., Koessler, A., Bouton, N.: Singularity analysis and reconfiguration mode of
the 3-CRS parallel manipulator, IEEE International Conference on Robotics and Automation (ICRA), Paris, France, (2020).
3. Gogu, G.: Structural synthesis of parallel robots, Dordrecht: Springer Netherlands (2008).

20

Survey of Graphic Software for teaching Mechanism
Synthesis using Path Curvature Theory
Mohan Nagrurkara, P. S. Deoleb, P. B. Shiwalkarc
a,b,c

1

Shri Ramdeobaba College of Engineering and Management, Nagpur-13, India
shiwalkarpb1@rknec.edu

Introduction and need

Wider choice of rigid body mechanisms for creating compliant mechanisms is overdue [1]. Approximate straight line linkages, as a family, are focused in this discussion.
Inflection Circle (IC), on its’ own, and in unison with the Cubic of Stationary Curvature (CSC) are two main strengths for teaching Mechanism Synthesis. Today there are
negligible takers for these concepts [2]. Using commonly visible applications, interestin these concepts can be rekindled [3]. To achieve this, eight different graphic softwares are compared for usability towards this goal.

Fig. 1.Graded levels of tracing and quantification of straight paths21

2

Methodology

Eight listed graphic software suitable for teaching the concepts at three levels of understanding are in Fig.1. Table 1 shows only seven features out of twenty technocommercial features. Concepts of level 3 (yellow path) are more involved comparedto level 1 (red path) and level 2 (blue path). Six features of kinematic analysis (notincluded here) are noted to be of help in further research.

Mech
Analyzer

SAM
8.2

Linkage

ams-

view
GI

M
An

B

L

C

L

L

B

L

B







-



-

-

Input [Lengths (L)/Coordinates (C)/Both(B)]3

Can it draw ICs at various crank positions



-

-

-

Can it draw a cubic of stationary curvature?



-

-

-

Output [Graphical(G)/Coordinates(C)/Both(B)]B

Export to AutoCAD (dwg)Export coupler curves values to Excel

Mechanism Library

-

C

G

G









-







-

G

alytixWorking
Model
2D

AutoCADSOFTWARESFEATURES

Ad

Table 1.Abridged set of features listed for used softwares

G

G

G

-





-

-

-

-

-



-

-

-

Conclusion

With proper selection of the graphic software with appropriate background processing
capacity, academic interest in the apparently complex concepts of IC and CSC can berekindled to reap the proper benefits.

References
1. Zhao K. and Schmiedeler J.P.: Using Rigid-Body Mechanism Topologies to Design Path
Generating Compliant Mechanisms, Journal of Mechanisms and Robotics, February 2016,
Vol. 8 (2016)
2. Torres-Moreno J., Giménez-Fernández A.: Carbone G. and Ceccarelli M., Kinematic andDynamic Analysis of Old Mechanism by Modern Means, The 14th IFToMM World Congress, Taipei, Taiwan, October 25-30, 2015, DOI: 10.6567/IFToMM.14TH.WC.PS7.001(2015)
3. Shiwalkar P.B. and Padole P.M.: Revisiting Inflection Circle Via Level Luffing Crane for
Academic Revival, HMM 2022, HMMS 40, pp 255-265, doi:10.1007/978-3-030-984991_21 (2022)

22

Comparative Combustion Characteristics of Dimethyl
Ether and Diesel Fueled Engines
Shanti Mehra, Hardikk Valera, Vikram Kumar, Avinash Kumar Agarwal*
Engine Research Laboratory, Department of Mechanical Engineering
Indian Institute of Technology Kanpur, Kanpur-208016, India*Corresponding Author: akag@iitk.ac.in

1

Introduction

Compression ignition (CI) engines are used for various functions ranging from transportation and power generators to agriculture equipment and machinery. Conventional
diesel engines are efficient and have good fuel economy but have higher emissions of
nitrogen oxides (NOx) and particulate matter (PM). DME is a promising fuel for CI
engines since it has a high cetane number and an inbuilt oxygen atom in its chemical
structure. The chemical properties of DME lead to a shorter ignition delay and almost
negligible soot emissions. Therefore, this study conducted experiments on a direct injection, mechanical injector type, in-line three-cylinder CI engine. The test fuels were
DME and diesel. DME exists as a gas at normal room temperature conditions and isliquified when pressurized above 5 bar [1]. DME has a high vapor pressure, low lubricity, and a lower calorific value. Therefore, the fuel injection system was modified forthe injection of DME into the engine cylinders. The engine speed was fixed at 1200
rpm, and the engine load was varied from no load to 6.47 bar BMEP.
1.1
Fuel Line Pressure
DME has a low liquid density, higher vapor pressure, and higher compressibility.
Therefore, the pressure build-up in the high-pressure fuel lines differs from that of diesel.
1200 RPM
550
450

Diesel1.29 bar BMEPDMENo Load350
250Line Pressure (bar)

150
50
550
450

2.59 bar BMEP

3.88 bar BMEP

5.18 bar BMEP

6.47 bar BMEP

350
250
150
50
550
450
350
250
150
50
-20

-10

0

10

20

30

-10

0

10

20

30

Crank Angle (degree) Crank Angle (degree)(a)(b)
Fig. 1 (a) Fuel Line Pressure (b) In-cylinder pressure vs crank angle for 1200 rpm engine speed23

It can be seen in Fig.1(a) that DME had a longer injection delay and injection duration
than diesel. This was because the quantity of DME injected was almost 1.5 times diesel
to maintain the same energy density input as diesel. Also, DME had pressure oscillations and a higher residual pressure in the high-pressure line because the higher compressibility of DME leads to more energy storage in compressed DME during its injection [2].
1.2

Combustion Characteristics

The in-cylinder pressure was lower for DME than diesel because of the lower calorificvalue of DME. Also, the latent heat of vaporization is higher for DME [3]. The peak of
HRR was higher for diesel than DME in the premixed combustion phase. The sharp
rise in the CHR curve was delayed for DME. This was due to the longer injection delay
for DME. The CHR was higher for DME after the steep rise. The combustion duration
was shorter for DME.
1.29 bar BMEP

DME

240

2000

180

1500

120

1000

60

500

3.88 bar BMEP

2.59 bar BMEP

-60

Heat Release Rate (J/°CA)

0

180

120
60
0

5.18 bar BMEP

6.47 bar BMEP

-60

180

-60

-40

-20

0

20

40

Crank Angle (degree)

60

-40

-20

0

20

40

Crank Angle (degree)

1200 rpm
DieselNo Load1.29 bar BMEP

DME

0

Cumulative Heat Release (J)1200 rpm
DieselNo Load2000

2.59 bar BMEP

3.88 bar BMEP

5.18 bar BMEP

6.47 bar BMEP

1500
1000
500
0
2000
1500

120

1000

60

500

0

0

-60
60

-30

-15

0

15

30

45

Crank Angle (degree)

60

-15

0

15

30

45

60

Crank Angle (degree)(a)(b)
Fig. 2 (a) HRR and (b) CHR vs crank angle for 1200 rpm engine speed

The mixing-controlled phase dominated DME’s combustion. The lower calorificvalue of DME led to the injection of higher fuel quantity, leading to an increased
injection delay. However, the shorter ignition delay of DME due to its higher cetane
number led to the accumulation of lower fuel quantity and, therefore, lower heat releaseduring the premixed combustion phase. Additionally, the DME-fuelled engine hadhigher thermal efficiency, lower combustion noise, and almost smokeless combustion,
thus proving to be a promising alternative to conventional diesel engines.

References
1. Arcoumanis C, Bae C, Crookes R, Kinoshita E. The potential of dimethyl ether (DME) as
an alternative fuel for compression-ignition engines: A review. Fuel, 87(7):1014-30. (2008)
2. Kapus P, Ofner H. Development of fuel injection equipment and combustion system for DI
diesel engines operated on dimethyl ether. SAE Technical Paper (No. 950062) (1995)
3. Sorenson SC, Glensvig M, Abata DL. Dimethyl ether in diesel fuel injection systems. SAE
Transactions.; 438-49 (1998)

24

Design and Efficiency Analysis of 3K Paradox Planetary
Gear Drives
Qi-You Zhuang 1 and Shyi-Jeng Tsai 1 [0000-0002-7874-7943]
1 National Central University, Jhong-Li District, 320 Taoyuan City320, Taiwan

sjtsai@cc.ncu.edu.tw

1

Introduction

In multi-stage planetary gear mechanisms, the so-called “paradoxical planetary gear
mechanism” is commonly used for high speed ratios. The 3K-PPGT type often employs
two ring gears with small tooth differences and multiple identical planetary gears meshing with them. However, this type of planetary gear mechanism presents a complex
geometric calculation problem because the planets mesh simultaneously with two different sized ring gears. On the other hand, the PPGT mechanism generates backflow ofpower inside the mechanism, which increases power loss and causes a decrease in transmission efficiency. When used as a speed increasing mechanism, it can even result in
self-locking. The gearing data used in this study are presented in Table 1.
Table 1. Gearing data of study case.
Tooth number
Speed ratio
Number of planets
ModulePressure angle [deg]Face-width [mm]Center distance [mm]

2

S
25

A1
-47

P1
11

P2

A2
-41

20
40

20
20

20.68
6
2
20
40

20
20
36

Non-Standard Profile Design

In this study, the direct tooth profile design method was adopted by utilizing the concept
of complementary tooth profiles. The design parameters were selected as the toothcrown height and the working addendum circle tooth thickness, while the standard tooth
cutting tool system was excluded, and the design was directly performed using involute
tooth profiles. Design limitation equations, including tooth tip interference, toothflank/root interference, and contact ratio, were established based on gear pairs, and design charts were created, Fig.1. Then, the geometric parameters of the gear were obtained based on the optimal load capacity relationship between gear pairs using thetooth root strength calculation formulae in ISO 6336. The profiles are shown in Fig.2.

3

Efficiency Calculation

In this study, the power loss was calculated using relationships such as power balance
and torque balance, and an efficiency analysis matrix for multi-stage planetary gear
mechanisms was established. On the other hand, based on the planetary gear set analysis model established by Tsai et al. [1, 2], it was expanded into a load calculation matrix25*太陽齒輪齒冠高係數
factor of sun gear haPS
Addendumfor the PPGT, and the loads and corresponding gear torques affected by friction on eachcontact tooth pair were calculated, and the instantaneous meshing efficiency and transmission efficiency of the mechanism were derived. In the study, the efficiencies forboth reducer and increaser applications were analyzed. Fig.3 and Fig.4 show the power
flow and instantaneous efficiency analysis results with different friction coefficients 
for increaser application, respectively [3].
Annulus 1

A1 Tip interference limit

A1-P

0.4
A2 Pointing limit

0.3

0.2

Planet

A2-P

0.1
P Pointing limit

0
0.3

0.6

0.9

1.2

1.5
Sun

*
太陽齒輪工作節圓齒厚係數
Tooth thickness
factor of sun gear swSiFig. 1. Designchartparameteri i  7i9of.0  profile速增 0.97
 0.97 0.97 

Fig. 2. Designed Profiles

1

1

0

0

0

1

i
i2 2i210i2

13  tuoP
Pout Pout31% 31%
Pout  %
31%

S1 S1

S
S1

S1

S2 S2

2

732.4%%5612
2145%
2145%2145%

傳動效率

Pout= 3.2%
%8623
3299%
3299%3299%1175.8%

1179%
%9923
3268%
3268%3268%

S2S

S2

1

2165%
2165%2165%%
5412
730.4%

1123%
1123%1123%%3211
1 1134%1134%%4311134%
446.6%
445.4%
2211%
2211%2211%%0012
683.3%
A1 A1

A1

A
A1

2100%
2100%2100% 784.5%
%1122

C1 C1

2

2211%
2211%2211%%0022

C
C1 C2C1
2C 2

783.3%%
1  nP
P0in0=100%
i

C2

A2 A2
2200%
2200%2200%%1122

CC2
1

1229.9%

A
A2

A2

1

784.5%P P100%
 100%
P  100%
1229.9%3334%
3334%3334%%4333334%
3 3334%3334% %4333

Mesh
Power
嚙合功率
嚙合功率
率
功嚙合功率
部外

in

in

in

Coupling
Power 外部功率
External
外部功率
外部功率 Power
耦合功率
耦合功率
率功
合嚙
率耦合功率
功合耦

Fig. 3. Power flow and magnitude

4

Annulus 2

S-P

0.5

100%
100
80%
80
60%
60
40%
40
20%
20
0%
0
-20%
-20
-40%
-40
-60%
-60
-80%
-80
-100%
-100

μ = 0.05

Efficiency [%]

增速
增速 增速

0.6

μ = 0.15

μ = 0.25

0

0.1

0.2

0.3

0.4

0.5

Input
Rotation Angle [deg]輸入轉動角度[Deg]Fig. 4. Instantaneous efficiency: increaser

Conclusion

In this study, the direct tooth profile design method was used to successfully solve thedesign problem. From efficiency analysis results, the variation amplitude of the meshing efficiency during operation and reduces the impact of the direction change of thefriction force can be reduced, when PPGT with sequential mesh phase. The efficiencyof the 3K-type mechanism is about half that of the traditional serial planetary gear
mechanism, and the reduction will be greater in the case of acceleration. When thefriction coefficient is greater than 0.15, the gear mechanism will be self-locked.

References
1. Tsai, S.-J. and Zhuang, Q.-Y.: Analytical approach for load sharing analysis of a differential
type three-stage planetary gear drive. In proceedings of MPT2017-Kyoto, (2017).
2. Tsai, S.J., Huang, G.-L. and Ye, S.-Y.: Gear meshing analysis of planetary gear sets with afloating sun gear. Mechanism and Machine Theory, 84 (2015)
3. Müller, H. W. Die Umlaufgetriebe (The Planetary Gear Drives). Springer-Verlag Berlin
Heidelberg (1998).

26

Gear tooth topology modification with consideringhoning wheel dressing in power gear honing
Quoc-Duy Nguyen 1[0000-0001-7418-8884] and Yu-Ren Wu 2[0000-0001-5856-2944]
1,2 National Central University, Zhongli District, Taoyuan City, Taiwan (R.O.C)

yurenwu@ncu.edu.tw

Abstract. The dressing process in the power gear honing process is critical tocorrect and reshape a honing wheel with abrasion. However, there is a marked
lack of considering this process. In view of this, this study proposes a closed-loop
gear tooth topology modification method for power gear honing, consideringboth dressing and honing processes. A dressing gear is generated by the modified
rack cutter, which is utilized to reshape the honing wheel profile and then applied
to finalize the work gear. The expected tooth modification is achieved by theadditional motion derived from the combination of the sensitivity matrix and theLevenberg-Marquardt algorithm. A numerical result of a double-crowned helicalgear tooth is presented to prove the practicality of the proposed model.
Keywords: gear honing, dressing process, topology modification.

1

Introduction

The gear-honing method enables high production efficiency [1]. Although there aremany previous studies evaluating the advantages or exploring methods to achieve
crowned gear tooth surfaces during honing process [2-5], however, none of them investigated the issue of honing wheel dressing. Therefore, this study proposes a methodof gear tooth topology modification with considering dressing and honing processes for
CNC power gear honing.

2

Proposed method

As shown in Fig. 1, the modeling procedure in this research is illustrated. The
mathematical model of dressing and honing processes are established based on a CNC
gear honing machine. A dressing gear with a barreled shape tooth is used to reshape thehoning wheel, which is then used to hone the work gear tooth to achieve the required
tooth modification by adding additional motions in the machining axes of the CNC
machine. A sensitivity matrix relating to the dressed amount and the additional motions
is constructed to determine the corresponding values of dressing and honing settings
for the required work gear tooth profile using the Levenberg-Marquardt algorithm. To
see the geometry difference between the corrected honing wheel and the modified work
gear, their tooth surface topographies with the normal deviation are presented.

27

Dressed honing
wheel surface

Honed gearsurfaceFig. 1. Procedure of gear tooth modification considering both dressing and honing processes.

3

Numerical examples and discussions
Tooth thickness

Unit: μm

24.97
Tooth space

90.45
F

94.23
H

90.53
K

102.6

24.27
A

20.33

106.4

G

20.36

B
C

24.55

I

E

1

(a)

24.65

D

102.7

2

B

T

3

O

O

T

P

4

1
2
3
4

5

5

6
6

7

7

8
9

102.6

102.7

(b)

8

90.45

106.4

24.27 24.97

94.23

Normal deviation on
dressed honing wheel

20.36

90.53

24.65

20.33

Normal deviation
on honed gear

9

24.55

(c)

Fig. 2. (a) basic inputs; (b) normal deviation for the target work-gear tooth surface, and (c) calculated results of normal deviation on the honing wheel and work-gear tooth surfaces.

A numerical example is presented to show how to achieve a double-crowned work-gear
tooth surface using the proposed method. As shown in Fig. 2(c), the honing wheel isapproximately dressed by 90~107 μm, and those normal deviations at corners on the
double-crowned gear surface are very close to the target crowning value of -25.00 μm.
The result proves the practicability of the proposed method.

References
1. D.T. Mehta and M.G. Rathi, A review on internal gear honing, Int. J. Eng. Res. Technol.
2(5) (2013) 973-983.
2. V.Q. Tran and Y.R. Wu, A novel method for closed-loop topology modification of helicalgears using internal-meshing gear honing, Mech. and Mach. Theory 145 (2020) 103691
3. V.Q. Tran and Y.R. Wu, Dual lead-crowning for helical gears with long face width on a
CNC internal gear honing machine, Mech. and Mach. Theory 130 (2018) 170-183.
4. J. Han, Y.G. Zhu, L. Xia, and X.Q. Tian, A novel gear flank modification methodology oninternal gearing power honing gear machine, Mech. and Mach. Theory 121 (2018) 669–682

28

Load sharing in planetary transmissions affected by
eccentricity and index errors in the sun
J. Sanchez-Espiga1[0000-0001-8413-3561] A. Fernández-del-Rincón1[0000-0001-6999-0776], M.
Iglesias1[0000-0003-3557-0647], A. De-Juan1[0000-0003-3583-1624], P. García1[0000-0003-4856-3155],
G. Huo1,2, F. Viadero 1[0000-0002-6483-1802]
1 Universidad de Cantabria, Santander, Cantabria, 39005, Spain
2 Harbin Institute of Technology, Harbin, China

viaderof@unican.es

1

Introduction

Planetary gear transmissions are a crucial component in the power transmission of systems such as vehicles, aircrafts [1] and wind generators [2]. This importance comesfrom their advantages compared to other gear transmissions, the power density, compactness, robustness and coaxiality between inlet and outlet. These transmissions also
provide the opportunity of increasing the number of planets to augment its power density. However, the number of elements that compose the transmission bring more possibilities for manufacturing errors [3], [4] too. Thus, this work focuses on the impact
some of those manufacturing errors have in the performance of the planetary transmissions where they belong.
The errors that are considered in this precise work are time-dependent errors present
in the sun gear. More precisely, these errors are eccentricity and index errors.
Therefore, this work focuses on the impact these errors have the in the geometry of
the contact between the sun gear and the planets that surround it. Then, these changes
have an impact directly on the transmission’s load sharing.

2

Load sharing

In this work, a 2D hybrid model developed by the authors following Vedmar’s proposal[5] and presented in [6] is employed to model the behavior of Equally Spaced In-Phase(ESIP) and Equally Spaced Sequentially Phased (ESSP) planetary transmissions.
This model uses a hybrid approach to solve the contact between gears and finds thebalance in the transmission in order to be able to analyze the behavior of these transmissions under a series of working conditions.

3

Influence of the time dependent errors in the load sharing

The errors are modeled following a sinusoidal formulation, such as the one presented
in [7]. This formulation agrees with the manufacturing process followed to cut the29

gears. In addition, this formulation allows the comparison between the impacts of both
errors in the same transmission.
Thus, the importance of this analysis comes from the impact that these errors havein the transmission’s performance. Firstly, due to their nature this impact varies withtime. Therefore, starting by the eccentricity error it means that the gear is not rotatingwith respect to its geometrical center, but at a distance of that point. As the gear rotates,
this error is going to change its role, from tangential mounting error to radial error or a
combination of both. Thus, these errors will change their importance in the load sharing[8] and modulations appear.
On the other hand, the index error refers to the difference between the actual positionof a tooth and its ideal position. Therefore, the error will vary from generating andadvancement to a delay in the contact between the sun gear and the planet i. Thus, there
will be a modulation also in the load sharing ratio variation in the transmission due tothis change.

References
[1]
[2]

[3]

[4]

[5]

[6]

[7]

[8]

J. Kurzke, “Fundamental differences between conventional and geared
turbofans,” Proceedings of the ASME Turbo Expo, vol. 1, pp. 145–153, 2009.
H. Aurrekoetxea and I. R. De Ocenda, “Experimental and theoretical study ofload mesh factor for different boundary conditions in wind gearbox planetary
stages,” in International Conference on Gears 2019, VDI Verlag, 2019, pp.
835–844.
A. Bodas and A. Kahraman, “Influence of Carrier and Gear Manufacturing
Errors on the Static Load Sharing Behavior of Planetary Gear Sets,” JSMEInternational Journal Series C, vol. 47, no. 3, pp. 908–915, 2004.
A. Kahraman, “Static Load Sharing Characteristics of Transmission Planetary
Gear Sets : Model and Experiment,” Transmission and Driveline Systems
Symposium, no. 1, pp. 1–10, 1999.
L. Vedmar and B. Henriksson, “A General Approach for Determining Dynamic
Forces in Spur Gears,” Journal of Mechanical Design, vol. 120, no. 4, p. 593,
1998.
M. Iglesias, A. Fernandez del Rincon, A. de-Juan, A. Diez-Ibarbia, P. Garcia,
and F. Viadero, “Advanced model for the calculation of meshing forces in spur
gear planetary transmissions,” Meccanica, vol. 50, no. 7, pp. 1869–1894, 2015.
A. Fernández-Del-Rincón, M. Iglesias, A. De-Juan, A. Diez-Ibarbia, P. García,
and F. Viadero, “Gear transmission dynamics: Effects of index and run out
errors,” Applied Acoustics, vol. 108, pp. 63–83, 2016.
J. Sanchez-Espiga, A. Fernandez-del-Rincon, M. Iglesias, and F. Viadero,“Influence of errors in planetary transmissions load sharing under different
mesh phasing,” Mechanism and Machine Theory, vol. 153, p. 104012, Nov.
2020.

30

An Analytical Model for Power Skiving Process of HelicalFace Gears
Khoe-Qui Le1 and Yu-Ren Wu1 [0000-0001-5856-2944]
1 Department of Mechanical Engineering, National Central University, Taoyuan City 320317,

Taiwanyurenwu@ncu.edu.tw

Abstract. Nowadays, face gears are machined by gear shaping or gear hobbing.
Several studies have been conducted on applying gear skiving processes to generate “straight-tooth” face gears. Even so, a skiving methodology to manufacture“helical-tooth” face gears is not proposed yet. This study proposes a mathematical model for manufacturing helical face gears using the power skiving process.
A helical skiving cutter is generated using a corrected rack. The cutting path on
the CNC machine is then adjusted by adding additional motions in forms of polynomials. A skiving simulation is performed to attain the face gear surface withthe specified polynomial coefficients. The Levenberg-Marquardt algorithm andsensitivity matrix are employed to calculate the polynomial coefficients to attainthe accuracy requirement of the gear surfaces. The numerical results have verified the practicability of the proposed method.
Keywords: Helical Face Gear, Power Skiving, Sensitivity Matrix.

1

Introduction

Power skiving is an efficient cutting process to continuously cylindrical gears [1]. In
addition, many researchers studied the skiving process of spur face gears [2-4]. Therelacks studies of applying the skiving process on helical face gear. In view of this, thispaper presents the application of power skiving for generating helical face gear to improve the processing time and gear quality.

2

Mathematical model for generation of skiving cutter

Figure 1 shows an illustration of the skiving process used in this study. Based on a CNC
skiving machine, a mathematical model of the face gear skiving process is established.
A corrected rack is used to generate the power skiving, which is then used to manufacture the helical face gear by adding additional movements in the machining axes of a
CNC machine. The Levenberg-Marquardt algorithm and sensitivity matrix are employed to calculate the polynomial coefficients to attain the accuracy requirement of
the gear surfaces. The tooth surface topologies with normal deviations are presented toverify the practicability of the proposed method.

31

ys

Skiving
cutterysxg

Helical gear

Cx

5%

10%

Os ,1,2

xs

zf

Os

C

xg

Og
zg

zs

Cy

yf
Of

Helical face gearxs
x1

Skiving cutter
Cs

C

Cz

y3

C



xf

7 8
5 6
2 3 4
5%

y 4 , z3

Of

Cz

x3,4

9

Helical face gear
Theoretical gear
skiving tooth surface
tooth surface
1 2 3 4 5 6 7 8 9

z4, f

C

zg
zs

1

Cx

O3,4, f

e

C

Cy

x2

xg

Og

10%

z2

zs ,1

Helical face
gear

xf

xs

Os

s

y1,2

A

y3

C

Normal deviation

E

B

D

Fig. 1. Helical face-gear skiving process with considering the modified cutter profile and the
additional machining-axis motion.

3

Numerical examples and discussions
0.48
5.24

5.53
Outer

Unit [μm]
4.84

B
O
T
T
O
M

(a)
Helical gear
Helical face gear
6.52

e

Inner
2.88

5.81
4.06

(b)

101.6
96.44
Outer
101.2
100.8

1.41 103.5

7.58

5.26

Non-grinding
process

9
8
7
6
5
4
3
2
1

97.26
B
9

O

8

T

7

T

6

O

5

M

4
3
Inner
102.5
98.77
101.8

3.83

(c)

100.1

2

101.2

Grinding
allowance

1

99.84

Fig. 2. (a) design parameters; (b) skived helical face-gear assembled with its mating helical gear;(c) results of normal deviation with and without considering grinding allowance.

An example is presented to show the skiving simulation results of helical face gears fortwo desired cases: the accuracy grade B5 (ANSI/AGMA 2009-B01 standards) with amaximum deviation on the skived tooth flanks smaller than 7.5 µm (case 1) and theeven grinding stock of 100 µm on the skived tooth flanks (case 2). The results indicatethat the skived face gear flanks satisfy the desired designs. It is validated the practicability of the proposed model.

References
1. T.-T. Luu and Y.-R. Wu, "A novel correction method to attain even grinding allowance in
CNC gear skiving process," Mech. Mach. Theory, vol. 171, p. 104771, (2022).
2. H. Guo, T. Ma, S. Zhang, N. Zhao, and A. Fuentes-Aznar, "Computerized generation andsurface deviation correction of face gear drives generated by skiving," Mech. Mach. Theory,
vol. 173, p. 104839, (2022).
3. Z. Han, C. Jiang, and X. Deng, "Machining and meshing analysis of face gears by powerskiving," J. Adv. Mech. Des. Syst. Manuf., vol. 16, no. 1, pp. JAMDSM0002–
JAMDSM0002, (2022).
4. S. Mo, S. Wang, B. Luo, H. Bao, G. Cen, and Y. Huang, "Research on the skiving technology of face gear," Int. J. Adv. Manuf. Technol., vol. 121, no. 7–8, pp. 5181–5196, (2022).

32

Designing a Spur Shaper Cutter for a Non-Involute
Circular Spline
Yun-Hao Cheng1 and Yi-Cheng Chen1[0000-0001-7886-3680]
1 National Central University, Taoyuan 320, TAIWAN

ethan@ncu.edu.tw

1Spur Shaper Cutter Design

1.1

Introduction

Circular spline (CS), along with flex spline and wave generator, is one of the major
components of harmonic drives. This article presents a designing process for a spur
shaper cutter to produce a non-involute CS, Firstly, a given profile of a non-involute
CS was expressed by a B-spline curve via curve fitting. Then the shaper cutter wasderived based on the shaping mechanism [1], the provided CS [2] as well as the theory of gearing [3].
1.2

Shaping Mechanism for CS

A spur shaper cutter resembles a pinion with tapered teeth along the axial direction,and thus is commonly called a pinion cutter. Besides, rake angle, tip relief angle andside relief angle are usually necessary on the shaper cutter for the chip removal purpose and cutting force consideration. Fig. 1 illustrates the kinematic relationship between a spur shaper cutter and a CS which exhibits internal teeth. The pinion cutter
and the CS respectively possess external and internal spur teeth.

Fig. 1. The shaping process by using a spur shaper cutter to produce a CS.

33

1.3

Numerical Example

Fig. 2 depicts the designed and generated tooth profiles of the CS. As revealed by
Fig.2, the designed CS and the generated CS profile have negligible deviations. Morespecifically, the maximum deviation between the generated profile and the designed
one is less than 1 μm, as shown in Fig. 2, which validates the correctness of the derived shaper cutter corresponding to the proper CS production.

Fig. 2. Designed CS profile and the CS profile generated by the shaper cutter.

Acknowledgement
The authors would like to thank the National Science and Technology Council of
Taiwan for finally supporting this research under grant NSTC 111-2221-E-008-073MY2.

References
1. Tsay, C.B., Liu, W.Y., Chen, Y.C.: Spur gear generation by shaper cutters, J. of Mat. Proc.
Tech. 104(3), 271-279 (2000)
2. Cheng, Y.H., Chen, Y.C.: Design, analysis, and optimization of a strain wave gear with anovel tooth profile, Mech. Mach. Theory 175, 104953 (2022).
3. Litvin, F.L., Fuentes, A.: Gear geometry and applied theory, Cambridge University Press,
New York (2004).

34

Ferdinand Freudenstein’s Spatial Kinematics
Pierre Larochelle
South Dakota School of Mines & Technology, Rapid City SD 57701, USA,
Pierre.Larochelle@sdsmt.edu,

Prof. Ferdinand Freudenstein is widely recognized as the Father of Modern
Kinematics [3, 4]. He made innumerable contributions to the field, one of which is
the training of future researchers. By the end of 1965, Dr. Freudenstein had graduated his first cadre of doctoral students from Columbia University that would
go on to become world-class researchers and leaders in kinematics. These doctoral graduates included George Sandor (1959)1 , Bernard Roth (1962), Ronald
Phillip (1964), A.T. Yang (1964), and Armand Dilpare (1965). In 1966, and soon
thereafter, a second cadre was studying with Prof. Freudenstein: Frank Buchsbaum (1967), Leo Dobrjansky (1967), Don Wallace (1968), Ralph Dratch (1970),
Steve Dubowsky (1971), and Mark Yuan (1972).
In this paper we examine in detail an advanced graduate-level course taught
by Prof. Freudenstein that bridged these first two cadres of doctoral students.
In the autumn term of 1965, Prof. Freudenstein taught ME E8405 Spatial Kinematics at Columbia University. In Figure 1 the detailed description of this course
from the Columbia University Bulletin is shown [2]. This would be Dr. Armand
Dilpare’s last term at Columbia University. Dr. Dilpare was a non-traditional
student, having worked in industry for several years before beginning his doctoral
studies. In his practice of engineering, Dr. Dilpare developed an appreciation for
detail and advanced abilities in engineering graphics. He employed these skills
when taking detailed and meticulous notes in his courses at Columbia University. Upon his retirement from the Florida Institute of Technology in 1994, Dr.
Dilpare donated his course notes to the author. An example of his course notes,
on the Euler-Savary Equation on a Sphere, is shown in Figure 2. In this paper we
examine the contents of Dr. Freudenstein’s advanced graduate course in spatial
kinematics through the lens of Dr. Dilpare’s detailed course notes.

Fig. 1. ME E8405 Course Description [2]1

The year the doctoral degree was awarded is listed in parenthases.

35

Fig. 2. Example from ME E8405 Course Notes [1]Acknowledgments The late Dr. Armand Leon Dilpare is gratefully acknowledged
for giving his detailed and illustrated ME E805 Spatial Kinematics fall 1965
course notes to the author. Dr. Ferdinand Freudenstein is whole-heatedly acknowledged for his founding of modern kinematics and for inspiring generationsof kinematicians around the globe.

References
1. Dilpare, A.: Course Notes ME E8405 Columbia University Fall 1965.
2. Columbia University: School of Engineering and Applied Sciences Bulletin 19651966, Columbia University. New York, NY. Series 65, Number 5, May 28, 1965.
https://findingaids.library.columbia.edu/ead/nnc-ua/ldpd 14621921/dsc
3. Erdman, A.G.: Modern Kinematics: Developments in the Last Forty Years. John
Wiley & Sons, 1993. ISBN 9780471554592.
4. Roth, B., In Memory of Professor Ferdinand Freudenstein, 1926–2006, ASME Journal of Mechanical Design, Volume 129, Number 3, Pages 241–242, March, 2007.

36

A New Design Method for Thick-panel Origami
Rui Peng1 and Gregory Scott Chirikjian1
1 National University of Singapore, Singapore 119077, Singapore

mpegre@nus.edu.sg

1

Introduction

Origami has great potential for applications in multiple fields [1]. However, it is complex and challenging to apply origami in some application circumstances, especiallythose with strong requirements of using thick materials to keep motion accuracy andstructure robust.
Modifying the origami pattern first and then using the altered origami pattern tobuild a thick origami structure is a unique method to accommodate the thickness.
Based on this concept, Ku and Demaine split every crease in a pattern into two creases [2], but the smooth surface of the origami pattern is broken with additional holes
and more difficult to fold. These problems can only be avoided for specific symmetricorigami patterns using Hull and Tachi’s approach [3] or just splitting parts of creases[4,5]. Those approaches have strict geometrical requirements for the target origami
patterns. They can only be applied to symmetric origami patterns, but there is no such
limitation in this presentation. Thus, references [2-4] cannot achieve any physicalthick panel models built in this presentation. Moreover, by using this presentation’s
approach, any origami patterns containing one or more of the three basic patterns
proposed in this presentation can be used to build thick panel structures.
In this presentation, we propose a novel thickness-accommodation approach. The
thick-panel origami structure built by our methods is one-degree-of-freedom with alarge fold-deploy ratio and has no holes. Besides symmetric patterns, the approach isalso suitable for more general origami patterns, such as the double-corrugated pattern,square-twist pattern, and general Miura-ori pattern. Besides flat patterns, this method
can also be used for origami tubes.

2

Main concept

The inherent problem of thickness accommodation is to avoid the collision between
adjacent facets induced by no allowance along the creases, which is more challenging
for flat-foldable patterns. However, folding from a flat state to another flat state
makes the pattern very advantageous with a large fold-deploy ratio. The basic conceptof this presentation is to modify the flat-foldable vertex to a non-flat-foldable vertex
but keep the original vertices' motion features. The basic concept of this presentation
is to convert a flat-foldable pattern into a quasi-flat-foldable pattern and use the quasiflat-foldable pattern to build thick origami structures [6].

37Fig. 1(a) is the square-twist pattern. According to the rules in this presentation,transfer it to the quasi-flat-foldable pattern in Fig. 1(b). Then a thick panel structure in
Fig. 1(c) is built based on Fig. 1(b). Compared with photos of the original pattern, itscorresponding quasi-flat-foldable patterns, and thick-panel structure, it is seen that
their folding motions are the same.

Fig. 1. (a) The original square-twist pattern. (b) The corresponding quasi-flat-foldable pattern.
(c) The corresponding thick-panel structure.

3

Conclusion

This presentation has proposed a technique for building thick-panel structures fromflat-foldable origami patterns. These structures maintain the folding motion of theoriginal origami patterns. They also have large fold-deploy ratios and very compact
folded states. This technique is applicable to any patterns constituted by the threebasic two-vertex patterns proposed in this presentation.

References
1. J.S. Dai, J. Rees Jones, Mobility in metamorphic mechanisms of foldable/erectable kinds,
Journal of Mechanical Design, 121 (1999) 375-382.
2. J.S. Ku, E.D. Demaine, Folding flat crease patterns with thick materials, Journal of Mechanisms and Robotics, 8 (2016) 031003.
3. T.C. Hull, T. Tachi, Double-line rigid origami, arXiv preprint arXiv:1709.03210, (2017).
4. K.A. Tolman, R.J. Lang, S.P. Magleby, L.L. Howell, Split-vertex technique for thicknessaccommodation in origami-based mechanisms, International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, American
Society of Mechanical Engineers, 2017, pp. V05BT08A054.
5. K.A. Tolman, Developing hybrid thickness-accommodation techniques for new origamiinspired engineered systems, Brigham Young University, 2017.
6. R. Peng, G.S. Chirikjian, A methodology for thick-panel origami pattern design, 2023.
(Under review)38

A tensegrity-based elastic joint element
Lukas Merker*, Valter Böhm, and Lena Zentner*Technische Universität Ilmenau, Germany,lukas.merker@tu-ilmenau.de,
WWW home page: https://www.tu-ilmenau.de/1

Introduction

In design engineering, it is frequently beneficial to couple components elastically, e.g., compensating for geometrical misalignment [1] or providing passive
vibration control [2]. Within this paper, we present an elastic tensegrity-based
joint element (TJE) according to Fig. 1(a). Even though similar structures are
already commercially available as toys, art sculptures, or pieces of furniture,they are rarely realized as compliant structures and, if so, the ability of thesystem to undergo significant deformations often remains unconsidered. In contrast, we suggest exploiting pre-stressed highly elastic tension members to realize
a compliant structure and analyze its deformations under different load cases [3].
Our investigation includes the analysis and modeling procedure of the TJE, theidentification of important system parameters as well as numerical simulations
to clarify the stiffness behavior of the TJE.

2Modeling

The 3D structure in Fig. 1(b) consists of two rigid compression members (CMs),each of which includes four nodes. The nodes are pairwise connected by fourcylindrical linear elastic tension members (TMs) with cross-sections Ai , Young’s
moduli E and original lengths l0i . We consider one CM as fixed in a global frame(0, x0 , y0 , z0 ), and the other one as displaced along with a local frame (Ω, x, y, z)
under the inference of an external load. The final position of the displaced CM−→
is described using the vector ⃗r0 = 0Ω and the classic Euler angles α, β and γ:⃗r0 = (rx , ry , rz )T ,(⃗ex0 , ⃗ey0 , ⃗ez0 )T = T(α, β, γ)(⃗ex , ⃗ey , ⃗ez )T(1)

According to (1), six unknown parameters define the overall shape of the structure, including the lengths and orientations of all TMs, see Fig. 1(b):⃗li = ⃗r0 + T(α, β, γ)⃗bi − ⃗ai ,li = |⃗li |,⃗ei = ⃗li /li(2)

In (2), ⃗ai and ⃗bi are the position vectors of the nodes i = 1, ..., 4 defined w.r.t.
the global and local frame, respectively. For any external force f⃗ and/or externali
moment m⃗ acting at Ω, the arising tensile forces f⃗i = EA
ei of the TMs
l0i (l0i − li )⃗are used to express the equilibrium conditions in the deformed state:⃗0 = f⃗ +

4
X
i=1

f⃗i ,

⃗0 = m⃗ +4
XT⃗bi × f⃗i

(3)

i=1

39

As (3) includes six scalar (nonlinear) equations and six unknown parameters, see(1), it is well defined and can be solved numerically to find the deformed shapeof the structure for any given load state, e.g., see Fig. 1(c).

Fig. 1: (a) TJE in a reference configuration (RC); (b) mechanical model in RC;(c) deformed configuration (DC); (d) displacement ∆⃗r0 , γ caused by m.
⃗

3

Results and Discussion

Inspired by the physical model in Fig. 1(a), we choose an exemplary structurewith b=h=l0i |i=1,...,3 =:l0 , l04 = l20 and E·Ai |i=1,...,3 =:E·A= 13 ·E·A4 , see Fig. 1(b).
For sake of conciseness, we limit the consideration to the x0 -y0 -symmetry planehere. Figure 1(c) qualitatively shows the deformed configuration of the structure
for the example of an external moment m⃗ = m ⃗ez0 acting at Ω. Figure 1(d)shows the displacement vector ∆⃗r0 = (∆xΩ , ∆yΩ )T and angle γ plotted againstm ∈ [−0.4, 0.4]·E·A·l0 . It becomes clear that the deformation of the structure
is approximately symmetrical for positive and negative moments with ∆x andγ changing approximately linear with the external moment. In this way, weinvestigate the deformation of the TJE in further non-symmetry planes in thecontext of different load cases, including both external forces and moments. The
presented model serves as a basis for parameter studies to show that the stiffness
behavior of the structure is significantly affected by the parameters b and h, seeFig. 1(b) as well as by the lengths l0i . In this way, we demonstrate that thepresented TJE offers tunable mechanical properties. Moreover, we highlight theadvantages that the TJE is scalable, easy to manufacture and to duplicate and,thus, cascadable both in serial or parallel arrangement.

References
1. Smith, S. T.: Flexures: elements of elastic mechanisms. Crc Press (2000)
2. Bian, J., Jing, X.: Analysis and design of a novel and compact X-structured vibration
isolation mount (X-Mount) with wider quasi-zero-stiffness range. Nonlinear Dyn.,
101(4), pp. 2195-2222 (2020)
3. Vega, J. C., Schorr, P., Kaufhold, T., Zentner, L., Zimmermann, K., Böhm, V.: Influence of elastomeric tensioned members on the characteristics of compliant tensegrity
structures in soft robotic applications. Procedia Manuf., 52, pp. 289-294 (2020)
We acknowledge the support by the DFG within the SPP 2100 projects ZE714/14-1, BO4114/3-1.

40

Coupler curves of a tendon driven hybrid rigid-flexible
four-bar. Applications to optimal path design
Alfonso Hernández1, Aitor Muñoyerro2, Mónica Urizar1, Oscar Altuzarra1
1 Faculty of Engineering of Bilbao, University of the Basque Country UPV/EHU. Plaza Torres

Quevedo 1, Bilbao 48013, Spain
2ITP Aero – Zamudio, Parque Tecnológico nº300, 48170 Vizcaya, Spain

Contact author: monica.urizar@ehu.eus

Unlike rigid link mechanisms, where positions can be determined by taking into account the geometry and configuration of the joints through a purely kinematic analysis,compliant mechanisms require the consideration of elasticity to define their configuration [1]. Therefore, a deformation model of the mechanism’s parts must be considered
together with the forces and moments applied to it by its own actuators and the external
environment. This makes obtaining closed-form solutions of classical kinematic problems a difficult task. In [2], the authors develop an approach consisting of using tendon
actuated bars to drive parallel kinematic mechanisms. In this case, the kinematic analysis problem of the parallel robot 3-RF[b]R has been tackled by taking advantage ofthe simplifications introduced by working with deformable bars of constant curvature.
A flexible actuated bar of this type will replace the crank input of a four-bar hinged
linkage of rigid elements. The resulting mechanism will be used to study the geometryof the curves generated by a coupler point. Now the input is the tendon’s curvature, κ,instead of the angular orientation of the crank. Figure 1 shows the parameters and variables representing the kinematics of such a hybrid mechanism.

Fig. 1. Kinematics parameters of the Tendon Driven Hybrid Rigid-Flexible Four-Bar

41

The first part of this work consists of characterizing the coupler curves of this mechanism. We have studied the composition of the coupler curves in circuits, and within
circuits the existence of one or more branches, following a pattern similar to [3]. Depending on the existence and location of the blocking positions, three different cases
can occur. These is described and analyzed in detail, highlighting fundamental differences in comparison to the rigid four-bar. In fact, the paths of these hybrid frigid-flexible mechanisms can include "open" circuits, more than two circuits and there are no(closed) circuits with only one branch.
In the second part, the knowledge related to these paths is implemented in an optimization algorithm, based on the gradient of the error function. Two objectives are pursued. The first one is to avoid circuit and branch errors. To do this, the optimization
algorithm must know, at each iteration, in which circuit and in which branch the coupler-point is located. The second target is to integrate the characterization about the
number and type of circuits that make up the path into the optimization algorithm. The
idea is that optimization process ceases to be a “closed box”, being able to use thisknowledge in an intelligent way to get the best solution. The examples carried out on
dimensional synthesis of path generation show the effectiveness of this new optimization algorithm. A very good quality of solutions is obtained, considering the possibilities offered by this simple mechanism. In addition, the algorithm guarantees mechanisms free of circuit and branch errors, typical of this type of synthesis.

Acknowledgments
The authors wish to acknowledge the financial support received from the Spanish
Government through the Ministerio de Ciencia e Innovación (Project PID2020116176GB-I00) financed by MCIN/AEI/10.13039/501100011033 and the support for
the research group through Project IT1480-22 provided by the Departamento de Educación from the Regional Basque Government.

References
1. L.L. Howell, S. P. Magleby, B. M. Olsen (Eds.). Handbook of Compliant Mechanisms. Wiley (2013).
2. S. Lilge, K. Nuelle, G. Boettcher, S. Spindeldreier, J. Burgner-Kahrs. Tendon Actuated Continuous Structures in Planar Parallel Robots: A Kinematic Analysis.
Journal of Mechanisms and Robotics 13 (2021) 011025.
3. A. Hernández, A. Muñoyerro, M. Urízar, E. Amezua. Comprehensive approach forthe dimensional synthesis of a four-bar linkage based on path assessment and reformulating the error function. Mechanism and Machine Theory 156 (2021)
104126.

42

Genetic Algorithm Application in Walking Mechanism
Designed with Planar Link Mechanism
Yoshihiko Matsumoto and Yasuhiro Inoue[0000-0002-1968-8883]
Kyoto University, Kyoto 615-8540, Japanmatsumoto.yoshihiko.t65@kyoto-u.jp

1

Introduction

Link mechanisms are essential in industries for enabling complex motions with simple
structures and providing accurate performance under high-speed conditions. Traditional design methods of link mechanisms involve discretizing the desired trajectoryand solving closed-loop equations at each point [1]. This study presents a new design
method using a genetic algorithm specifying the desired task as an input. Our proposed
method is applied to design a walking mechanism, and we present actual design result.

2

MethodIn this study, we determine how to assemble the link mechanism and extract the parameters necessary for assembly, and define a relationship between the parameters and genotypes. The genetic algorithm incorporates the minimal generation gap [2] and islandmodels to improve the preservation of genetic diversity. Physical simulations are conduced to evaluate the fitness.

3

Results

A physical simulation environment was created to test link mechanisms, considering
the possibility of collisions between links and pins. The fitness of a link mechanism
was defined as the distance the mechanism could move a slider when the driving link
was rotated at a constant speed and torque for a duration of 60 seconds in the simulation
environment. The termination criteria were set at 100,000 generations.
The walking mechanism was designed 100 times, and the results were classified into
two clusters using the expectation-maximization algorithm [3] (Fig.1 a). The mechanisms that belong to high-fitness cluster categorized based on their structure pattern and
Fig.1 (b) shows the best-fitted design for each pattern. Fig. 1 (c) depict the movementsof the upper-right pattern mechanism shown in Fig. 1 (b). Fig. 1 (d) shows the trajectories of the ground points of mechanisms shown in Fig. 1 (b). Despite structural differences, mechanisms with links connected to the same side of the main body exhibited
similar movements.

43

Fig. 1. (a) Histogram of the best fitness in each of the 100 design runs. (b) Best individuals pereach structure pattern of high-fitness cluster. (c) Movement of the mechanism upper-right pattern in (b). (d) Superimposed trajectories of the seven mechanisms shown in (b). The red andgreen lines are the trajectories of the first and last points to be grounded, respectively.

4

Discussion

In this study, we successfully generated a walking mechanism using a genetic algorithm. The generated mechanisms consist of a mixed population with both low and highfitness. Notably, we observed a variety of structures within the high-fitness group, despite the single-objective optimization. This observation led us to recognize the potential for proposing a new strategy for multi-objective optimization. Our approach focuseson obtaining diverse solutions through multiple calculations instead of a single computation. The underlying idea is that, by generating numerous solutions without imposing
restrictions on secondary objectives and evaluating fitness solely based on the primaryobjective, we can extract a solution from the diverse population that satisfies multiple
objectives. We believe that this approach is now feasible due to the significant advancements in computing power.

References
1. Freudenstein, F.: Approximate Synthesis of Four-Bar Linkages. Trans. ASME 77, 853–861(1955).
2. Satoh, H., Yamamura, M., Kobayashi, S.: Minimal Generation Gap Model for GAs Considering Both Exploration and Exploitation. Proceedings of 4th International Conference on
Soft Computing, 494-497 (1996).
3. Dempster, A. P., Laird N. M., Rubin, D. B.: Maximum Likelihood from Incomplete Data
via the EM Algorithm. J. Royal Stat. Society. Series B (Methodological) 39(1), 1-38 (1977).

44

Friction-induced redundancy of constraints and its
consequences
Marek Wojtyra1[0000-0001-7225-7647] and Janusz Frączek1[0000-0001-8232-5439]
1 Warsaw University of Technology, IAAM, Nowowiejska Str. 24, 00-665 Warsaw, Poland

Marek.Wojtyra@pw.edu.pl

1

Introduction

In many multibody modeling cases, the rigid body assumption is often adopted because
it has many advantages, mainly in terms of model complexity and computational efficiency. However, there are limitations of this approach—associated with redundantconstraints presence—which become particularly important when modeling friction effects. When friction that depends on normal reactions in joints is present in an overconstrained multibody system, the simulated motion of the system may be non-unique.
The present study shows that redundant constraints—with all their unavoidable consequences—may be introduced to the model by the frictional locking of the joints. Two
distinct approaches to static friction modeling are examined: (1) constraints additionand deletion [1] and (2) adding static friction as an active force governed by the adopted
friction model (e.g., the smooth Coulomb or LuGre [2]). It is indicated that in the latter
case, uniqueness problems evolve into parametric sensitivity problems.

2

Research and results

A mechanism described by n coordinates forming vector q, subjected to m non-redundant constraints Φ(q) = 0m1, is analyzed. It has one or more kinematic loops and morethan one DoF (d = n–m > 1). The generalized forces of sliding friction are introduced
as external loads relying on normal joint reactions [1], [3].
In the constraint addition-deletion method [1], static friction in the appropriate joints
is represented by additional driving constraints Ψ(q) = 0, imposed when the relative
velocity reaches zero. In the 1-DoF case, relative motion in all joints stops simultaneously, and constraints Ψ are added to all joints with friction. If the number of constraints
Ψ exceeds the number of DoFs, the mechanism becomes redundantly constrained [3].
Mind that the non-uniqueness of calculated joint reactions—and hence of friction
forces—is a direct consequence of the constraints’ redundancy. Further, detection of
stiction to sliding transition becomes impossible.
The situation is more intricate for mechanisms with many DoFs, and several distinct
cases must be analyzed. A particular case occurs when relative velocities vanish in several kinematic pairs simultaneously, and k scalar constraint equations are added,
whereas the number of the system’s DoFs decreases by less than k, and the mechanism
becomes overconstrained (with all unwelcome consequences).

45

The constraint addition-deletion method is rarely used. Stiction is more often introduced in terms of active forces rather than constraints. Usually, stiction and sliding
modes are modeled uniformly—the same equations (highly nonlinear at close to zero
relative velocities) are used for both friction modes. In article [3] (limited to closedloop chains with exactly one DoF), it was shown that—at the vicinity of the stiction
regime—solution non-uniqueness and high parametric sensitivity occurs when mechanisms with joint friction but without redundant constraints are modeled. In the present
study, we show that the earlier results regarding the outcomes of frictional locking may
be generalized to the case of closed-loop systems with many DoFs, under the condition
that particular relations within the kinematic structure exist. Examination of the kinematic properties of the mechanism alongside the equations depicting the friction model
reveals the reasons for the high parametric sensitivity and, therefore, the low credibilityof the simulation results. For the smooth Coulomb and the LuGre model, we show
that—in the stiction regime and its vicinity—the obtained results hinge on some secondary parameters, usually arbitrarily set to satisfy certain numerical needs.
For some mechanisms, the simultaneity of frictional locking of several joints (leading to sensitivity or uniqueness problems) is unavoidable since this property is embedded in their kinematic structure and dimensions. Hence an apt method for the mechanism’s structure investigation was devised. In brief, the fact that allowable generalized
velocities of a mechanism belong to the nullspace of the constraint Jacobian matrix is
utilized. The dependencies between relative velocities in joints are investigated by adding suitably selected driving constraints Ψ to geometric constraints Φ, determining thenullspace of [ΦTq (q) ΨTq (q)]T , and performing specific geometrical calculations.

3

Conclusions

The uniqueness problems—encountered in certain classes of mechanisms when static
friction is represented by additional driving constraints—evolve into difficulties withhigh parametric sensitivity when the stiction regime is modeled by active forces rather
than constraints. This contribution analyzes the foundations of these problems, and amethod for investigating the kinematic structure—to check if the problematic issues
may arise—is devised.
Acknowledgments. This research was supported by the National Science Centre,
Poland grant no. 2022/45/B/ST8/00661.

References
1. Haug E. J., Wu S. C., Yang S. M.: Dynamics of mechanical systems with Coulomb friction,
stiction, impact, and constraints addition-deletion. Mechanism and Machine Theory, 21(5),
401–425 (1986).
2. Marques F., et al.: A survey and comparison of several friction force models for dynamic
analysis of multibody mechanical systems, Nonlinear Dynamics, 86(3), 1407–1443 (2016).
3. Wojtyra M.: Modeling of static friction in closed-loop kinematic chains—Uniqueness andparametric sensitivity problems. Multibody System Dynamics, 39(4), 337–361 (2017).

46

A Study on a Method for Maintaining Contact
During Capture of Space Debris
with an Magneto-Rheological Damper
Ryogo Mizuno1 , Satoko Abiko2 , and Teppei Tsujita3
1

Graduate School of Engineering and Science, Shibaura Institute of Technology,
3-7-5 Toyosu, Koto-ku, Tokyo 135-8545, Japan
ma22137@shibaura-it.ac.jp
2
Department of Electrical Engineering, Shibaura Institute of Technology,
3-7-5 Toyosu, Koto-ku, Tokyo 135-8545, Japan
abiko@shibaura-it.ac.jp
3
Department of Mechanical Engineering, National Defense Academy of Japan,
1-10-20 Hashirimizu, Yokosuka, Kanagawa 239-8686, Japant.tsujita@ieee.org

1

Introduction

According to [1], five debris removals per year are required for sustainable space
utilization. Capturing large debris with a robot arm is considered one of theremoval methods [2]. In this method, contact force must be reduced during
capture so as not to push the target away. However, the momentum of thetarget depends on its size and state. Therefore, it is required to deal with themin the capture operation. This paper proposes debris capture with a double-rod
Magneto-Rheological (MR) damper that generates a variable damping force asshown in Fig.1.

2

Modeling of a Double-rod MR damper

The MR damper is a device whose damping force is varied by changing the flow
resistance of the MR fluid filled in the damper. This rheological property can becontrolled by changing the magnetic field applied to the MR fluid. The principleof operation of the double-rod MR damper is modeled based on [3].

3

Dynamics Simulation for Debris Capture

The equations of motion for the chaser, MR damper and target are formulated
and dynamics simulations are performed as shown in Fig.1. The simulations are
performed using the numerical software MATLAB/Simulink from The MathWorks, Inc. In the simulation, the debris approaches the chaser satellite andimpacts the end-effector connected to the MR damper. In the simulation, thesatellite and the end-effector weigh 100 kg and 10 kg, respectively. The debris

47

Chaser satellite

DebrisMR damper
S

Pressure

Force
N

Oil
MR fluid
Ferromagnet particle
Coil
Fluid flow
Magnetic flux

Fig. 1. Assumption of debris capture and MR damper mechanism

approaches the satellite with a relative velocity of 1 m/s. The debris weights are
10, 50, 100, 500, and 1000 kg. The four types of dampers are simulated. The firstis an MR damper with no magnetic field applied, and its damping coefficient isapproximately 150.8 Ns/m (Type 1). The second is an MR damper that controls
the applied magnetic field by current during the collision. The reference impulse
is the momentum the MR damper should accumulate so that the relative velocity between the chaser and target becomes zero. When the ratio of the impulse
at time t to the reference impulse is 0 or 1, the current is set to 0 A. When theratio is 0.95, the current is set to the maximum value. The current is changed
along a 5th-order spline curve that satisfies these conditions (Type 2). The thirdand fourth are linear dampers, with damping factors of 150.8 Ns/m (Type 3)
and 600.0 Ns/m (Type 4).
In the simulation, the smaller the damping coefficient, the smaller the maximum damping force during contact, but the longer the stroke length. In thissimulation, the stroke length limit of the dampers is set to 0.20 m. In the type
1 and type 3 simulations, the damper reached its stroke limit when the target
weighs 50 kg or more. In the simulation, the larger the damping coefficient, theshorter the stroke length, but the larger the maximum damping force. In the type4 simulation, the maximum damping force is greater than that of type 1 andtype 3. When the target weighs 1000 kg, the difference is about 650 N. Damping
force has a negative influence on the base of a satellite. Therefore, dampers are
required to reduce the maximum damping force within the possible stroke range.
In the type 2 simulation, the stroke length is within 0.20 m and the maximum
damping force is smaller than type 4, by changing the damping characteristicsof the MR damper. For instance, when the target weighs 500 kg, the difference
is approximately 350 N.
In the design of the MR damper for debris capture, it is required to havethe performance for capturing a wide range of target properties. The simulation
result shows the MR damper is promising to satisfy the requirement.

References
1. Liou, J.C.: An active debris removal parametric study for LEO environment remediation. Advances in Space Research, vol. 47, issue 11, pp. 1865-1876 (2011)
2. Papadopoulos, E., Aghili, F., Ma, O., Lampariello, R.: Robotic Manipulation andCapture in Space: A Survey. Frontiers in Robotics and AI, 8:686723 (2021)
3. Goldasz, J., Sapinski, B.: Insight into Magnetorheological Shock Absorbers. Springer(2015)

48

Experimental Determination of Calibrated Accuracy for
Six-axis Force and Torque Sensors Using Compliant
Mechanisms
Yu-Jen Wang1 and Shin-Yi Huang1
1 National Sun Yat-sen University, Kaohsiung 80424, Taiwan

yjwang@mail.nsysu.edu.tw

1

Introduction

With the popularity of robot arm applied in fabrication process and multi-axis loads
monitoring in machining, multi-axis force and torque (F/T) sensors have become key
components in the automated factory [1]. Accuracy and sensitivity of six-axis F/T sensor are crucial. Strain-gauge-based F/T sensors have high measurement accuracy, andis mainly suitable for static or quasi-static measurement. The design of the compliant
structure considers coupling effects, sensitivity and full span of the sensor. A compliant
mechanism composed of flexible links achieves force and motion transmission throughelastic deformation. The advantages of compliant mechanisms include without mechanical parts assembly, reduced friction and no backlash. A planar-type F/T sensor
using compliant mechanisms has strain gauges on the top or bottom surfaces only, without any strain gauges on the side surfaces to reduce the fabrication cost [2]. According
to aforementioned information, the axis decoupling structure, e.g. the dual-frame structure [3], has benefits on high decoupling results, but it is difficult to fabricate and attached with strain gauges. On the other hand, the axis coupling structure, e.g. the planartype F/T sensor, the main advantage is easy to fabricate, but the axis coupling effect isobvious. This paper will discuss the precision of the two F/T sensors using different
calibration data sets to find the suitable calibration process for the F/T sensors.

2

Structures of dual-frame F/T and planar-type F/T sensors

The structure of the F/T sensor is axisymmetric and consists of a dual frame with innerand outer elastic parts as shown in [3]. The planar F/T sensor is 120-deg-symmetricalabout the geometric center and consists of three limbs, as shown in Fig.1. The six-axis
force and torque sensor is based on 3-RRR (rotation) compliant mechanism [2]. Compliant mechanisms are mechanisms using flexible hinges instead of rigid joints. Forces
and torques are defined by the coordinate o at the end effector. Strain gauges S1 to S6
are used to sense Fx, Fy, and Tz, and are composed as V1 to V3. The strain gauges ofsensing plates on the top and bottom surfaces are diagonally connected in Wheatston
half-bridge circuit. The correspondence between the strain gauge pairs and the measured F/Ts was provided. The sensing plates are closed to pivot joints of each RRR
mechanism that enlarges the strains on the sensing plates.
Lever 1

Fz

Fy

Tz

Ty

Sensing
plate

Limb B

S5
U_S6

U_S8
S1 U_S2

Limb A

Lever 2
S7

Fx

y

Tx

Limb C

o

S11
U_S12

x

S9
U_S10
U_S4
S3

(a)

(b)

Fig. 1. Structure of planar six-axis force/torque sensor [2].
49

3Calibration process and results

The calibration machine was developed to provide six-axis independent and known
forces and torques to calibrate F/T sensors [4]. Calibration is performed for mapping
the relationship between the inputs and the outputs of a sensor. A transformation matrix
to convert the output signals (voltages) into the subjected F/T components is acquiredby using least square method. The calibration results are shown in Figs. 2 (a) and (b).
A total of 420 single-axis F/T sets that included a repeated measure for each axis with
10 N and 0.5 N-m intervals were used as training data. The six-axis data was composedby the single-axis data. The full-span loads of the F/T sensors were decided as Fx, Fy,
and Fz = ±200 N and Tx, Ty, and Tz = ±10 N-m. The test data sets are six axis data. Once
the F/T sensor with excellent super position (linear) behaviors, the calibration errors
using single- and six-axis data would be the same. Therefore, the two sensors havesome non-superposition behaviors. The mean errors of the dual-frame sensor using single- and six-axis data sets are 1.45% and 1.21% respectively. The mean errors of theplanar F/T sensor using the two data sets are 2.76% and 2.34% respectively. That shows
the dual-frame F/T sensor with better accuracy than the planar type F/T sensor. To test
the accuracy of the calibrated sensors, the testing data in Fig. 2 (c) are random six-axis
data sets that didn’t used in calculated the transformation matrix. The differences between Figs. 2 are insignificant. That shows the calibration process using six-axis data
sets are representative even tested by additional data sets. The accuracy of the dualframe F/T sensor is higher than that of the planar type F/T sensor. The calibration process in Fx, Fy and Tz should be checked or reworked. The calibration results of the two
types of F/T sensors are promising. Therefore, planar F/T sensors have good performance and easy fabrication advantage. The F/T sensor using compliant mechanisms
could be applied to the end effector of the robot arm to sense applied loads with highaccuracy.

1
0
Fy

Fz

Tx

Ty

Tz

Loads
Single axis F/T data sets(a)

Six axis F/T data sets

8
7
6
5
4
3
2
1
0

Errors (%)

Error (%)

Error (%)

2

Fx

8

Planar six-axis F/T sensor

Dual-frame six-axis F/T sensor
3

Fx

Fy

Fz

Tx

Ty

Six axis F/T data sets(b)

Planar-type F/T sensor

6
4
2

Tz

Loads
Single axis F/T data sets

Dual-frame F/T sensor

0
Fx

Fy

Fz
Tx
Loads

Ty

Tz

(c)

Fig. 2. Calibration errors using single axis and six axis data sets (a) for dual-frame F/T sensor
and (b) for planar six-axis F/T sensor. (c) Calibration errors tested by random six-axis data sets
for the two sensors.

References
1. I. Payo, J. M. Adánez, D. R. Rosa, R. Fernández, and A. S. Vázquez, “Six-Axis ColumnType Force and Moment Sensor for Robotic Applications,” IEEE Sensors J., 18(17), 69967004, (2018).
2. Y. J. Wang, L. C. Wu, J. D. Ke and T. F. Lu, “Planar Six-Axis Force and Torque Sensors,”
IEEE Sensors J., 21(23), 26631-26641, (2021).
3. Y. J. Wang, C. W. Hsu and C. Y. Sue, “Design and Calibration of a Dual-Frame Force andTorque Sensor,” IEEE Sensors J., 20(20), 12134-12145, (2020)
4. Y. J. Wang and C. W. Tung, “A machine for calibrating six-axis force/torque sensors using
a torque sensing structure and a stiffness compensation model,” Sensors and Actuators A:
Physical, 334(1), 113323, (2022).
50

The Effects of Passive Joints on the Stiffness of a Parallel
Kinematic Manipulator
Pin-Yi Ho1, Chia-Hsin Hsieh1, Wei-Hsuan Lin1, Chih-Wei Li1, Cheng-Kuo Sung1 andYu-Jen Chiu2*
1 National Tsing Hua University, Hsinchu 300044, Taiwan R.O.C.
2 Ming Chi University of Technology, New Taipei City 243303, Taiwan R.O.C.

yjchiu@mail.mcut.edu.tw

1

Introduction

Due to the inherent close-looped configurations, parallel kinematic manipulators(PKMs) are anticipated to possess higher stiffness and lower inertia than those with
serial-type mechanisms. Nonetheless, one of the important features of a PKM is that a
number of passive joints are essentially introduced. A passive joint will lose the abilityof resisting the force and moment along the direction of its degrees-of-freedom, thus
considerably deteriorating the precision of a PKM when external loads are applied. It
has been inferred as one of the causes that leads to geometrical discrepancies of PKMs[1]. The present work is aimed at the quantitative investigation into the passive joints
that influence the stiffness of a PKM. Both the analytical approach based on the matrix
structural analysis (MSA) [2] and the finite element analysis (FEA) by employing thecommercial software are introduced in this study. The proper orientations of the passive
joints installed are analyzed and suggested as well.

2

Methods

A translational 3-UPU configured PKM with variable-length links is considered in thiswork to investigate its elastostatic behavior. In Fig. 1, Each of the three linkage modulesof the PKM is dismantled into two universal joints Ai , Bi and one link Li ( i  1, 2, 3 ).
The universal joint is considered as two passive revolute joints with orthogonal axes.
The joint components and links are flexible with the corresponding 6  6 stiffness matrices, which are obtained by the ANSYS software. It is noted the stiffness matrix of
Li depends on the distance between Ai and Bi when the prismatic joint is actuated,while the end-effector is assumed to be rigid. By associating the stiffness matrices ofindividual components, an analytical MSA-based stiffness model of the whole PKM
can be achieved.

3

Results and Discussion

The translational and rotational stiffness values in X, Y and Z directions are shown in
Fig. 2. It indicates the translational stiffness in Z direction is significantly higher thanthat in X and Y direction by about 2 to 7 times. Contrarily, the rotational stiffness in Z
direction is much lower than that in X and Y directions. The averaged stiffness values
on the lowest and highest planes of the workspace are listed in Table 1. The stiffness of
the PKM under released and locked modes of the passive joints is analyzed and listed
in Table 1. It reveals that locking joints Ai enhances the translational stiffness in X and51

Y directions by over 40%. However, it also leads to a considerable decrease in the rotational stiffness along Z direction. Alternatively, when joints Bi are locked, a significant increase in the rotational stiffness is observed. The evidence assures the crucial
influences of the passive joints on the stiffness of a PKM. The optimal orientation of
the joint axes installed in a tilt angle of 35  40 from the vertical is also suggested.

(a)

(c)

(b)

Fig. 1. A 3-UPU type PKM: (a)the configuration; (b)the schematic diagram of the MSA-based
stiffness mode; (c)the stiffness analysis by adopting the FEM software.

Fig. 2. The average and extremum values of the translational and rotational stiffness of the PKM.
Table 1. The effects of the joint mobility on the stiffness of the PKM.
Direction
End-Effector’s Position*
Stiffness (N  m1 , N m rad 1 )Locking Joints Ai (%)
Locking Joints Bi (%)* L:

Trans. X/Y
L
H
34
84
40
45
10
12

Trans. Z
L
H
297
211
0
1
9
23

Rot. X/Y
L
H
22
15
11
-1
124
194

Rot. Z
L
H
9
11
-76
-30
167
230

Z  200 mm, H: Z  500 mm

Acknowledgement
This research was financially supported by the National Science and Technology Council, Taiwan. (NSTC 111-2221-E-007-068-MY2 and NSTC 112-2637-E-131-005). The
authors also appreciate the assistance of Ms. Yi-Syuan Lee in this work.

References
1. Tang, T. F., Zhang, J.: Conceptual design and comparative stiffness analysis of an Exechonlike parallel kinematic machine with lockable spherical joints. International Journal of Advanced Robotic Systems (July-August), 1-13 (2017).
2. Klimchik, A., Pashkevich, A., Chablat, D.: Fundamentals of manipulator stiffness modelingusing matrix structural analysis. Mechanism and Machine Theory 133, 365–394 (2019).

52

Toward Safe and Efficient Human-Robot Teams:
Mixed Reality-based Robot Motion and
Safety Index Visualization
Gustavo Alfonso Garcia Ricardez1 , Carl Törnberg2 ,Lotfi El Hafi1 , Jorge Solis2 , and Tadahiro Taniguchi1
1

Ritsumeikan University, Kusatsu 525-8577, Japan
Karlstad University, Karlstad 651 88, Sweden

2

1

Introduction

Human-robot collaboration (HRC) is essential to address workforce shortages inaging societies like in Japan and Sweden. However, current HRC lacks effective
synchronization between human and robot plans, leading to inefficiencies. Our
research aims to improve communication and synchronization using mixed reality (MR) and Artificial Intelligence (AI). MR will visually convey robot plans,
motions, and environmental data, while AI will interpret human input, generate
robot responses, and adaptively plan the next step, with decisions conveyed via
MR. Ultimately, we aim to test this framework in a collaborative assembly task,
evaluating efficiency, safety, and human-centered metrics. This abstract focuseson MR-based visualization for robot motion and human safety, aiming to balancesafety with efficiency.

(a) Setup.

(b) Workspace visualization.

(c) Workpiece occupancy.

(d) Safety index visualization.

Fig. 1: Proposed system.

53

2

Proposed System

Our proposed system’s hardware consists of a head-mounted display worn by thehuman and a robot arm with an end effector. The head-mounted display is theMicrosoft HoloLens 21 , the robot arm is the KUKA LBR iiwa 14 R8202 , whichis equipped with a custom-made end effector developed by the team NAISTRITS-Panasonic [1] for the Future Convenience Store Challenge, as shown in
Fig. 1a. The robot is placed on a fixed base, and the workspace where the task
takes place is also mounted on the base, as shown in Fig. 1b.
To display the robot’s motion, the visualizer component subscribes to the
topics corresponding to motion planning (i.e., MoveIt-related topics). From suchinformation, the robot’s goals are obtained and displayed to the human. Since
the shape of the manipulated objects is typically known from sensor information
or from a priori data, the object’s shape is also displayed to the human to depict
the soon-to-be-occupied region, as shown in Fig. 1c.
To display the human safety index, the visualizer component calculates thesafety index of the Asymmetric Velocity Moderation (AVM) [2] method, as
shown in Fig. 1d. AVM’s safety index is obtained from the angle between displacement vectors (i.e., vectors from points on the robot and points on the human) and velocity vectors (i.e., relative velocity vectors between those points),
as well as the distance between the human and the robot. In other words, AVM
considers not only the distance but also the direction of the motion.

3

Ongoing Experiments

We will subjectively evaluate the user experience by controlling the amount andstyle of the displayed information when interacting with the robot. To do this, weplace the human and the robot across a rectangular workspace. The robot picks
and places cubes between predefined positions, while a human moves within
the robot’s reachable range. Moreover, we will measure the safety index andthe proximity between the human and the robot. We expect to find the overall
preferred settings to obtain motion and safety information that reduces the safety
risks and allows the human to anticipate the robot’s motion.

References
1. Garcia Ricardez, G.A., El Hafi, L., Ikeuchi, H., Yamamoto, M., Takamatsu, J.,
Taniguchi, T., Ogasawara, T.: Team NAIST-RITS-Panasonic at the Future Convenience Store Challenge: Our Approach from 2018 to 2021. Journal of the Society of Instrument and Control Engineers (SICE) 61(6), 422–425 (Jun 2022),
https://doi.org/10.11499/sicejl.61.422
2. Garcia Ricardez, G.A., Yamaguchi, A., Takamatsu, J., Ogasawara, T.: Asymmetric
Velocity Moderation for Human-safe Robot Control. RSJ Advanced Robotics (AR)29(17), 1111–1125 (Sep 2015), https://doi.org/10.1080/01691864.2015.1034173
1
2

https://www.microsoft.com/hololens
https://www.kuka.com/products/robotics-systems/industrial-robots/lbr-iiwa

54

An Alternative Solution for Balancing of the
3-PRRR Fully-Isotropic Translational Parallel
Robot
Mario Acevedo1[0000−00002−1433−8147]
Universidad Panamericana. Facultad de Ingeniería.
Álvaro del Portillo 49, Zapopan, Jalisco, 45010, México.

The transmission of vibrations to the fixed frame, produced by the unbalanced
inertia forces, increase the shaking force and shaking moment. Removing or
decreasing these alternating dynamic loads is desirable. This has been solved indifferent ways. These methods generally imply a considerable increment in thesystem’s mass. A different approach, based on planning the displacements of thetotal CoM of the system, has been applied recently to balancing a fully-isotropictranslational parallel robot called orthoglide, [1].
In this work, this approach is resumed using fully Cartesian coordinates. A
method already applied for balancing a planar parallel manipulator, [2]. In thisway, joints are defined with no constraint equations while keeping moderate thenumber of variables. This modeling technique is applied for the balancing of the
3PRRR Fully-Isotropic Translational Parallel Robot, see Fig. 1, introduced in[3]. The expressions to calculate the general CoM, the shaking force, and theshaking moment of the system are obtained in a direct and automated way. The
force balancing conditions, directly expressed in terms of the local coordinates of
the CoM of the bodies, are obtained directly from the terms in the mass matrix,
contributing to making the optimal control of the robot-manipulator CoM fasterand easy to perform.
The global CoM (g), the linear momentum (l), and the angular momentum(h) are all expressed as a function of the system’s mass matrix and of the global
Cartesian coordinates:

mg = Mql = mġ = BMq̇h = q̃Mq̇

(1)
(2)
(3)

respectively. Where m is the system’s mass, ġ is the CoM velocity, M is thesystem’s mass matrix assembled from the mass associated with the basic points,
whose coordinates form the vector of positions q, and its derivative the vectorof cartesian velocities q̇. B is a matrix introduced here to arrange the terms ofthe matrix multiplication and is composed of (3 × 3) identity matrices. Finally,q̃ is a column vector representing the vector product of the position of eachbasic point times its corresponding linear momentum. These expressions areused for the force balancing of the mechanisms applying the method based on55

the optimal control of the global CoM of the manipulator. The acceleration of
the global CoM is reduced using the “bang-bang” law, proposing to partiallybalance the manipulator without adding supplementary masses.
The shaking force fsh , calculated as:
fsh = BMq̈(4)

and the shaking moment, which depends on the coordinate’s accelerations solely,obtained by:τ = q̃Mq̈
(5)
are used to verify the behavior of the mechanism before and after the force
balancing. All the procedure is illustrated through a numerical example, and theresults obtained are verified by simulation.

Fig. 1. A representation of the 3PRRR Fully-Isotropic Translational Parallel Robot.
Point P represents the end-effector.

References
1. Geng, J., Arakelian, V., Chablat, D., Lemoine, P.: Balancing of the Orthoglide
Taking into Account Its Varying Payload. Robotics 10, 30, (2021)
2. Acevedo, M., Orvañanos-Guerrero, M.T., Velázquez, R., Arakelian, V. An Alternative Method for Shaking Force Balancing of the 3RRR PPM through Acceleration
Control of the Center of Mass. Appl. Sci. 10, 1351 (2020)
3. Gogu, G. Structural synthesis of fully-isotropic translational parallel robots via
theory of linear transformations, European Journal of Mechanics - A/Solids, 23(6),1021–1039, (2004)

56

A Novel Approach to Occupancy Grid Map Merging inEnvironments with Highly Repetitive Features
Chung-Jui Lai and Kuei-Yuan Chan1
Department of Mechanical Engineering,
National Taiwan University, Taipei 10617, Taiwan,chanky@ntu.edu.tw

1

Background and Motivation

In this work, we focus on deploying a group of robots to explore a space and reconstruct
the map by sensing their surroundings and combining the information gathered. Individual
maps can be merged through direct or indirect methods, as overviewed by Lee [1]. Direct
methods, as described in [2], use multiple RGB images to compute the Map Transformation
Matrix (MTM) by matching common 2D visual objects detected by a camera. Although they
are not limited by environmental constraints, they require significant data storage. On theother hand, indirect methods use previously constructed maps for feature extraction andmatching to calculate the MTM, thus reducing storage requirements. However, in scenarios
such as large warehouses and factories where features extracted for map merging are highly
repetitive, existing methods, regardless of whether they are direct or indirect, are unable tobe effective. Fig.1 illustrates this issue, where a significant number of feature matches areincorrect, making merging impossible. We propose a modified map merging technique with
communication strength inspired by a mechanism to overcome this limitation. Several studies,including the case shown in Fig.1, are used to demonstrate how our approach works in detail.

Fig. 1. The diagram shows feature matching in a highly repetitive feature environment. Incorrectfeature matches are marked in red, resulting in failed map merging.

2

Proposed Methodology

Our proposed method utilizes communication signal strength to estimate the relative distance
between two robots and merge their maps by calculating the MTM based on the kinematic
motion analysis. The kinematic motion analysis treats two maps and relative distance atmultiple time points as a link with less than one degree of freedom to achieve map merging.
However, the MTM may contain inaccuracies due to signal noise. To detect errors in theMTM, we apply an Acceptance Index and modify Ferrão et al.’s feature method in [3] tocorrect the MTM if the error is unacceptable. This modification includes changing unique57

feature matching to non-unique matching and adding rotation/translation constraints in the
MTM calculation. Fig.2 shows the flowchart of our proposed process. As can be seen theprocess provides the merged map once the error of the corrected MTM is acceptable.

Fig. 2. Flowchart of proposed method.

3

Results and Discussion

Our proposed method was tested on four highly repetitive feature environments, and successful map merging results were obtained. One of the merged maps is shown in Fig.3. In
contrast to existing merging techniques, as shown in Fig.1, our method provides a resultwith an Acceptance Index of 0.9736. This indicates that 97.36% of the overlapped areas arecorrectly matched. The application of our method enables the deployment of multiple robots
with unknown initial locations in high repetitive feature fields. However, it should be notedthat our method requires the resolution of both maps to be the same.

Fig. 3. The merged result of highly repetitive feature maps in this study. Green represents same-color
overlaps, red represents different-color overlaps.

Acknowledgement
This work was supported by the National Science and Technology Council of Taiwan under
grant MOST 110-2221-E002-136-MY3.

References
1. Lee, Heon-Cheol, et al. ”A survey of map merging techniques for cooperative-SLAM.” 2012 9thInternational Conference on Ubiquitous Robots and Ambient Intelligence (URAI). IEEE, 2012.
2. Lee, H. C. ”Implementation of a network-based robot system for cooperative recognition andlocalization of multiple objects.” Proc. IEEK Summer Conf.. 2012.
3. Ferrão, Victor Terra, Cássio Dener Noronha Vinhal, and Gelson da Cruz. ”An occupancy grid
map merging algorithm invariant to scale, rotation and translation.” 2017 Brazilian Conferenceon Intelligent Systems (BRACIS). IEEE, 2017.
58

Human-Robot Collaboration Based on Robot Motion
Planning with Adaptive Obstacle Avoidance
Hao Jian Eugene Tong1, Brijesh Patel1, Yan-Cen Lin1, Zhi-Lin Zhang1, Chao-Yi Lin1,
Chao-Lung Yang2, Ching-Yuan Chang3, and Po Ting Lin1,4,*[0000-0001-5907-7828]
1

Department of Mechanical Engineering, National Taiwan University of Science and Technology, Taipei 10607, Taiwan
2
Department of Industrial Management, National Taiwan University of Science and Technology, Taipei 10607, Taiwan
3
Department of Mechanical Engineering, National Taipei University of Technology, Taipei
10608, Taiwan
4Intelligent Manufacturing Innovation Center, National Taiwan University of Science andTechnology, Taipei 10607, Taiwan*Corresponding Author’s email: potinglin@mail.ntust.edu.tw
Abstract. Human-Robot Collaboration (HRC) has the potential to revolutionize
various industries by improving performance, productivity, and safety. However,ensuring safety in the collaborative workspace is crucial. To address this, a classification system for safety standards for industrial robotics has been establishedby ISO 10218. This paper proposes a Human Robot Collaboration Index (HRCI)
to enhance efficiency, ability, and safety of human workers in scenarios where
current robots are inadequate. The HRCI system adjusts robots' safety thresholds
based on the specific task being performed, promoting productive and efficientcollaboration between humans and robots. The methodology involves using a 3D
camera for skeleton recognition of human motion, followed by the Spatial-Temporal Graph Convolutional Network (ST-GCN) to identify human motion sequence with the analysis of therbligs. The robot's movement speed and obstacle
avoidance threshold are adjusted based on the task at hand. When human motion
and robot movement are supposed to be close, robot movement slows down,
maintaining a lower but safe threshold of obstacle avoidance to enable gentle
contact with the human. Conversely, when humans should not be near the robot,
it maintains a higher level of obstacle avoidance and avoids contact. This approach optimizes the efficiency of robot motion and safety to the surrounding
workers and environment simultaneously. The proposed HRCI system offers apromising solution to the challenges posed by traditional collision avoidance
methods, promoting human-robot collaboration while ensuring safety.
Keywords: Human-Robot Collaboration (HRC), Spatial-Temporal Graph Convolutional Network (ST-GCN), Robot Motion Planning with Obstacle Avoidance.

1

Process Flow of the Proposed Method

As shown in Fig. 1, the proposed method was implemented in a Human-Robot Collaboration (HRC) application where a robot arm was to deliver an item to the human59worker. A 3D camera (RGBD) was utilized to capture the 3D skeleton of human motion
by mapping the acquired MediaPipe skeleton [1] to the 3D point cloud. The SpatialTemporal Graph Convolutional Network (ST-GCN) [2] was developed to classify thehuman motion based on the analyses of therbligs. A Human-Robot Collaboration Index(HRCI) was proposed to specify how the robot was supposed to work with human. The
following formulation [3, 4] was used to find the optimal robot trajectory with adaptive
upper limit of collision safety.
(1)
Min å x - x T,is.t. D(x, O) £ D
iwhere x is the design variable of robot joints; x T ,i is the i th point on the original trajectory; O is the coordinate of the obstacle; D is the danger level of collision; D is
the upper limit of danger level to be adaptively adjusted based on the determined HRCI.
Lower D keeps a greater safety distance between human and robot. Properly increased
value of D allows the robot to keep a closer distance from human, thus HRC could beappropriately achieved.

Fig. 1. Proposed method of robot motion planning with adaptive obstacle avoidance based on
Human-Robot Collaboration Index (HRCI).

References
1. Lugaresi, C., Tang, J., Nash, H., McClanahan, C., Uboweja, E., Hays, M., Zhang, F., Chang,
C.-L., Yong, M., Lee, J.: Mediapipe: A framework for perceiving and processing reality. In:
Third Workshop on Computer Vision for AR/VR at IEEE Computer Vision and Pattern
Recognition (CVPR), Long Beach, CA, USA (2019).
2. Yang, C.-L., Setyoko, A., Tampubolon, H., Hua, K.-L.: Pairwise adjacency matrix on spatial
temporal graph convolution network for skeleton-based two-person interaction recognition.
In: 2020 IEEE International Conference on Image Processing (ICIP), 2166-2170 (2020).
3. Lin, C.-Y.: Robot Arm Path Planning Based on Obstacle Occupancy Modeling andTrajectory Reliability Optimization. MS Thesis, Department of Mechanical Engineering,
National Taiwan University of Science and Technology, Taipei, Taiwan (2021).
4. Zhang, Z.-L.: Robot Arm Path Planning with Obstacle Aviodance Based on Obstacle
Occupancy Random Forest Model and Lagragian Minimization. MS Thesis, Department of
Mechanical Engineering, National Taiwan University of Science and Technology, Taipei,
Taiwan (2022).

60

Body Gesture Recognition for Collaborative Robots
Jorge Solis1[0000-0002-6865-7346], Koyu Nakamori1,
Gustavo Alfonso Garcia Ricardez2[0000-0001-6518-577X] and Johan Håkansson3
1Karlstad University, Karlstad, Sweden
2Ritsumeikan University, Kyoto, Japan

3Goodtech Solutions AB, Karlstad, Sweden

solis@ieee.org

1

Introduction

One of the main reasons for using collaborative robots is to improve the efficiency of
today’s manufacturing technology. They will increasingly work side by side withhumans, which requires a completely different safety paradigm. In this research, we
aim to implement novel sustainable solutions based on collaborative robots using
mixed reality and artificial intelligence.

2

Gesture Recognition System for Collaborative Robots

Gesture is one of the most well-known non-verbal communication tools by using
body motions. Hazegawa et al. [1] introduced a generic method that utilizes gaze andsurrounding environment information for recognizing grasp intention. Solis et.al. [2]developed a robot vehicle for carrying-medical tools with 3D gesture recognition
system by using time-delay neural network. In this work, we applied the 3D gesturerecognition system [2] for collaborative robots to send commands to the robot. This
will make workers more comfortable to work and we implemented a function to getrobot status (e.g. its speed, etc.) which enables a bi-directional human-robot interaction.

3

Integrated System Overview

The camera is installed on top of the IRB 14000 YuMi® (Fig. 1a). The height of thecamera is adjusted to show above a person's knees. The camera is connected to amini-PC, which is then connected to robot controller by an Ethernet cable.
We selected PC SDK because this is the most suitable to our work and easy to implement. PC SDK allows connecting to the robot controller and sending commanddirectly (see Fig. 1b) from PC to the controller by using methods written in C#. In
order to communicate the recognized gesture, we made a robot communication module to connect and send commands to the robot controller (Fig. 1a). We implemented
a simple assemble task to the robot. In this task, the robot grabs a cup with one handand an eraser with the other one and places the eraser inside the cup (Fig. 1a).

61

a)EngageDisengage

Follow

Stop

Connect tothe controller

Disconnect fromthe controller

Start RAPID
ProgramStop RAPID
Program

ComeRight

ComeLeft① Change Speed Ratio (Robot Running)-5%(Min 5 %)+5%(Max 20 %)② Change Pick Position (Robot Stopped)b)

Right Arm

Left Arm

Fig. 1. a) Integrated system overview, b) Mapping between recognized gestures and commands

4

Preliminary Experiments and Results

An experimental procedure was prepared in which all gestures were performed atleast once, and four volunteers were asked to perform it. The time taken for them tocomplete a proposed procedure was measured (engagecome rightcomeleftfollowstop). Each subject was asked to repeat the task three times and theresults are shown in Table 1. Subjects #2, #3 and #4 generally completed the testsmoothly, but subject #1 took significantly longer due to gestures were not being
recognized. However, the task took considerably less time the second and third times.
Table 1. Time for each volunteer to perform the procedure.
Trial

Subject 1

Subject 2

1st [min]

1:45

Subject 3
1:26

Subject 4
2:01

8:04

2nd [min]2:39

3rd [min]

1:29

1:24

1:49

2:00

1:57

1:32

1:54

References
1. Hasegawa, Y., et al., Natural grasp intention recognition based on gaze in human-robot interaction, IEEE journal of Biomedical and Health Informatics, vol. 27(4), pp. 2059-2070(2023).
2. Solis, J., Amaral, F. (2017). Denoising of human motion data for a 3D gesture recognition
system for a two-wheeled inverted pendulum robot, IEEE International Conference on
Advanced Intelligent Mechatronics, pp. 43-4

62

Stem detection using depth camera in red perilla
farm
Seito Takeuchi1 , Shunsuke Komizunai2 , Taku Senoo1 , and Atsushi Konno1
11

Graduate school of Information Science and Technology, Hokkaido University,
Sapporo, Japan,{takeuchi@scc, senoo@ssi}.ist.hokudai.ac.jp,
2
Faculty of Engineering and Design, Kagawa University, Takamatsu, Japan

Introduction

Since weeds have negative impacts on crop growth, weeding is an essential task.
When weeding with a robotic hand, part of a weed may remain depending on
the grasping position. Therefore, it is necessary to detect a stem of weed as an
appropriate grasping position. A method that uses deep learning to segment
weeds and detect stem positions [1] requires pixel-wise labeling of the images inthe dataset, which takes a lot of time and effort. This study proposes a methodthat detects a weed stem position using YOLOv7 [2] and image processing.

2

MethodThe proposed method has two stages. First, bounding boxes indicating weed
areas are extracted using YOLOv7. Segmentation is then performed on eachbounding box to separate the weeds from the background. Following this, image
processing is used to find the location of the stem. In this study, Intel RealSense
Depth Camera D435i was used to capture the RGBD images.
2.1

Weed detection using YOLOv7

One of the object detection methods, YOLOv7, was used for weed detection. The
object detection performance of YOLOv7 outperforms the conventional YOLO
series in both accuracy and speed. As both real-time performance and detection
accuracy are important for weed detection, YOLOv7 was selected for this study.
The model of YOLOv7 was trained with a total of 1000 images, 100 for eachspecies, for a total of 10 species of red perilla and 9 weeds observed on the farm.
2.2

Stem detection using image processing

From top left to bottom right, Figure 1 shows the process of stem detection after
weed detection. First, the green color of the weeds is extracted by specifying a
range of hues (a*) in the L*a*b* color space. Next, the leaves of the weed areseparated by gradually moving the outline of the weed inwards. Then each leaf is63

Table 1. Comparison of performance
MethodCenter of BBox
Line fitting
Proposed method

Precision

Recall

0.768
0.754
0.870

0.883
0.867
0.870

Fig. 1. Process of stem detection

fitted with a straight line. The coordinates of the centroid of the figure enclosedby these lines are taken as stem position 1. The area around the coordinatescorresponding to stem position 1 is then searched in the depth image and thenearest point is taken as stem position 2. Finally, the midpoint between stem
position 1 and stem position 2 is detected as the final stem position.

3

Results and Discussion

Precision and recall were used to evaluate the stem detection performance. To
verify the effectiveness of the proposed method, a comparison of the three cases
is shown in Table 1. From top to bottom, the results are shown when the centerof the bounding box is detected as the final stem position, when the result ofstem position 1 is detected as the final stem position, and when the proposed
method combining line fitting method and depth image search method is used todetect the final stem position. The proposed method achieved higher accuracy
by combining the two method than when using the center of the bounding box
as the final stem position or when using line fitting method alone.

4

Conclusions

In this study, a method of stem detection was proposed. The proposed method
detects weeds using YOLOv7, and then detects the stem position using only a
combination of simple image processing. This simplifies the preparation of thedataset compared to deep learning-based methods for detecting stem positions.
The accuracy of stem detection needs to be further improved in the future.

Acknowledgment
We appreciate the support of Mishima Foods Co., Ltd. and Hiroshima University.

References
1. X. Zhang, et al.: “A Unified Model for Real-Time Crop Recognition and Stem Localization Exploiting Cross-Task Feature Fusion,” 2020 IEEE International Conference
on Real-time Computing and Robotics (RCAR), pp.327–322, 2020.
2. Wang, C.Y., et al.: “YOLOv7: Trainable bag-of-freebies sets new state-of-the-art for
real-time object detectors.” http://www.ncbi.nlm.nih.gov

64

Vacuum-powered and fabric-based soft actuator
Lola Courty and Kenjiro Takemura
Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, Kanagawa 223-8522, Japan
takemura@mech.keio.ac.jp

In the past few years, pneumatic artificial muscles (PAMs) have been widely
considered in the field of soft robotics. Inherently compliant, they offer highspeed, large deformation and actuation stress, and high force to weight ratio ata relatively low cost. It therefore promises a safe and powerful actuation for a
multitude of applications. Usually, they involve a bladder that expands uponpressurization, with strain-limiting components to guide the deformation andachieve complex motions. Those PAMs operate with positive pressure. However,vacuum-powered artificial muscles (VAMPs) have recently gained interest as
they can exhibit equivalent range of motions, most often at larger contraction
ratios, in constrained space, hence offering greater safety and compactness. A
previous study [1] on VAMPs has introduced a Fluid-driven Origami Artificial
Muscle (FOAM) which consists of a compressible zigzag-like skeleton, encased ina tight nonstretchable skin. The role of the skeleton is to guide the deformationinduced by depressurizing the actuator, with the caveats that the skeleton canunpredictably buckle or slide, hindering its movement and force induced, as well
as reproducibility over extended use [2].
For this work, an improved version of FOAMs is designed and characterized,
having in mind an application in hand rehabilitation. The actuator proposed
here is a small fabric-based soft actuator, whose skeleton is fixed to both ends to
avoid sliding. It operates on low vacuum pressure (<80 kPa), and is, to mimic
the flexion of a hand joint, a bending actuator.
To manufacture the actuator, a skeleton is 3D printed using flexible resin(Flexible 80A, Formlabs). The design consists of an asymmetric zigzag; only
one side can contract while the other can merely expand. Then, it is inserted
into a TPU-coated nylon fabric tube (170 g/sqm), and a string is looped andtightened around both ends in grooves dug into the skeleton. Beforehand, tomake the tube, two sheets of fabric are cut, with one larger than the other, andheat sealed on both same-length sides. Traditionally, a single sheet is rolled andadhered to itself. We, however, heat-seal a sheet of fabric upon a flat shorter one
to easily creates a cavity into which the skeleton can be inserted. In addition,
it helps the bending movement by using the fabric inherent stiffness. Finally, an
air inlet is encased into one end of the skeleton and sealed using an adhesive(Aquaseal, GEAR AID) to avoid leaks.
The actuator is characterized in terms of angular displacement and blocked
tip force upon depressurization. The latter is realized via a 60 mL syringe
mounted on a motorized linear stage to achieve repeatable pressure values. To
determine the angular displacement, the actuator is hung, with a colored pin

65

Fig. 1. 45-mm actuator (A) components: air inlet (B), skeleton (C), thread (D), andfabric (E)attached to its other end to track the displacement. A camera is placed in frontof the actuator, perpendicular to the motion plane. The bending angle is definedas the angle between the tracked end initial and final positions, with the origin
set at the fixed end. The blocked tip force was measured by steadily increasing
vacuum, with a customized force measurement setup, inspired from a previous
study [3]. One end of the actuator is fixed, while the other is lying upon a weighting scale, and a constraining plate is placed above the actuator. Therefore, thenon-linear effects induced by bending are limited.
With a 45-mm actuator (Fig. 1), the bending angle reaches 50° at -50 kPa.
The displacements are consistent and reproducible, and a small hysteresis can beobserved when the actuator is repressurized to reach its initial state. To achievea larger bending angle, the skeleton must be longer: for instance, for a 100-mm
long actuator, 75° is reached at -50 kPa. The blocked tip force obtained at -50
kPa is about 1 N, and 1.4 N at -80 kPa for the 45-mm actuator. To increase theblocked tip force, the cross-section of the actuator can be enlarged.
This actuator is a demonstration of the FOAM concept: depending on thedesign of the skeleton, various motions can be achieved. Our new technique toclose the outer membrane with thread enables direct contact with the ends of theskeleton, therefore allowing personalized extrema, and facilitating the integrationof the actuator.

References
1. Li, S., Vogt, D.M., Rus, D., Wood, R.J: Fluid-driven origami-inspired artificial muscles. Proc. Natl. Acad. Sci. USA, 114, 13132–13137 (2017). doi:10.1016/
0022-2836(81)90087-5
2. Mendoza, M.J., Gollob, S.D., Lavado, D., Koo, B.H.B., Cruz, S., Roche, E.T., Vela,
E.A.: A Vacuum-Powered Artificial Muscle Designed for Infant Rehabilitation. Micromachines, 12, 971 (2021).doi:10.3390/mi12080971
3. Polygerinos, P., Wang, Z., Overvelde, J. T. B., Galloway, K. C., Wood, R. J.,
Bertoldi, K., et al: Modeling of soft fiber-reinforced bending actuators. IEEE Trans.
Robot. 31, 778–789. (2015) doi:10.1109/TRO.2015.2428504

66

Accuracy Criteria for Planar Flexures
Matteo Verotti, Simone Serafino, and Pietro Fanghella
University of Genoa
Department of Mechanical, Energy, Management and Transportation Engineering,
Via all’Opera Pia, Genoa, Italy 16145

In the last decades, compliant mechanisms have been widely implemented in avariety of precision engineering applications. While many studies focused on analysis and synthesis methods [1], limited results regarding the analysis of the accuracy
criteria have been presented. According to the rigid-body replacement method [2],the substitution of a revolute joint with a compliant element determines a relative
motion between the connected bodies that generally differs from the nominal rotation around the axis of the kinematic pair, phenomenon often called center or axis
drift. In literature, various criteria to evaluate the position accuracy of flexures havebeen proposed [3]. These criteria are briefly illustrated in Fig. 1 in case of a uniform
flexure, where the position accuracy is evaluated as the magnitude of the vector thatdefines the position of a specific point associated to the deformed configuration withrespect to the nominal center of rotation of the flexure, Cr , coincident to the trace ofthe revolute joint axis.
θE

θE

E
y

E

y
dT

O

θE

E

Cr T

(a)

E0
x

O

y
dF F
Cr

(b)

E0
x

O

C dC
Cr

E0
x

(c)

Fig. 1: Position accuracy criteria: end-section tangent (a), rigid-body (b), and pole ofthe displacement (c).
Figure 2(a) shows a cross-axis flexural pivot with straight flexure elements intersecting at their midpoint with crossing angle β = π/4 rad. Figure 2(b) reports thetrends of the end-section tangent, rigid-body, and pole of the displacement criteria
for a platform rotation up to ϕ = π/2 rad, evaluated by performing finite element
simulations with the commercial software Ansys.
The position accuracy criteria can be considered as a useful tool for designinghigh-accuracy compliant systems. The cross-axis pivot depicted in Fig. 2(a) is adopted
as a starting reference design to be improved, and the parameter dC is used to evaluate the system accuracy. In a previous investigation [4], it was demonstrated that accuracy of cross-axis pivots strongly depends on flexures initial curvature and orientation, represented through the design parameters 2α and β, respectively, in Fig. 3(a).
The study considered initially-curved elements positioned in such a way their centroids were coincident. Figure 3(b) shows the accuracy design map generated evaluα)ating the accuracy d(2and d(0)of the curved and straight pivots, respectively, for a
C
C

67

0.25

A0

B0

dT
dF
dC

0.2
0.15

F

0.1

Cr ≡ F0

0.05

π
β=
4

0

L0

R0

(a)

0

:/8

:/4
? (rad)

3:/8

:/2

(b)

Fig. 2: Cross-axis flexural pivot in neutral (solid) and deformed (ϕ = π/2, dashed)configurations (a); trends of accuracy parameters for increasing rotations ϕ (b).
platform rotation ϕ = π/4. Colored dots represent the α-β configurations for whichα) (0)
the ratio d̃ = d(2/dC < 1 , therefore determining an accuracy improvement with reC
spect to the straight case. It can be noted that accuracy improvements about 20% canbe achieved in the left-bottom region, for relatively small values of α and β. Higher
accuracy performance can be obtained in the right-upper region, that correspond tocurved cross-axis pivots with strong curvature and orientation. For example, the configuration with β̄ = 0.513 rad and ᾱ = 1.032 rad achieves an accuracy ratio d̃ = 0.74.
Hence, the corresponding curved cross-axis, reported in Fig. 3(a), is 26% more accurate with respect the straight cross-axis reported in Fig. 2(a).
A0

B0
y
x
α
β
α
L0

R0

(a)

(b)

Fig. 3: Curved cross-axis pivot with β̄ = 0.513 rad and ᾱ = 1.032 rad (a); accuracy design map corresponding to ϕ = π/4 (b), β and α in radians.

References
1. Liu, Y., Zhang, Z.: A large range compliant XY nano-manipulator with active parasitic rotation rejection. Precision Engineering 72, 640–652 (nov 2021)
2. Mattson, C.: Handbook of compliant mechanisms, chap. Synthesis through Rigid-Body Replacement, pp. 109–121. John Wiley & Sons (2013)
3. Verotti, M., Serafino, S., Fanghella, P.: Position accuracy criteria for planar flexural hinges.
Precision Engineering 80, 82–94 (2023)
4. Serafino, S., Fanghella, P., Verotti, M.: Initial curvature and centroid positioning effects oncross-axis flexural pivots accuracy. Mechanism and Machine Theory 177, 105039 (nov 2022)

68

Dynamic Task Capability based Task Allocation
for Collaborative Manipulation
Keshab Patra1, Arpita Sinha1, and Anirban Guha1
1 Indian Institute of Technology Bombay, Mumbai 400076, India,

Keshabpatra19@gmail.com

Collaborative mobile manipulators have an advantage over single manipulators fortasks requiring dexterity, e.g., transporting heavy or oversized payload and fixture-lessmultipart assembly. This advantage comes with the cost of complexity in robot coordination, communication, and task allocation, especially while manipulating an unknown
object in a cluttered environment. The manipulators should suitably share the task for
optimal task capability, resource allocation, and maximum fault tolerance. Hence it isessential to quantify the dynamic task capability of the individual members, the entire
group and allocate the task equitably. This work introduces a computationally efficient
cooperative task capability finding method and a corresponding dynamic task allocation scheme.
Task-space force and manipulability ellipsoids are defined [1] for cooperating manipulators grasping a rigid object where the task/load sharing among them is constantand predefined. It leads to inefficient utilization of the capabilities of the manipulators.
A coupled inverse dynamic-based technique has been reported for computing the dynamic load-carrying capacity of multiple cooperating manipulators in the joint space
using D’ Alembert’s principle [3], ignoring the inertia properties of the object and theend effector (EE). Analytical and optimization-based methods [2] for force capabilities
computation require high computational time and do not scale well when used for many
manipulators, making it incapable of real-time operation.
We reformulate the task capability finding formulation of the manipulator based on
the force polytope proposed by Yoshikawa [5] that defines the map between the joint
actuator torque 𝝉 and the external wrench 𝒉 at the EE is 𝑱𝑻 𝒉 = 𝝉. The task capabilityof 𝑖 − 𝑡ℎ manipulator is computed online using Eqn. (1) for each time instant as a scalarmultiplier 𝑘𝑖 of the desired wrench 𝒉𝒐 for the task completion in the task space considering the manipulator’s dynamics 𝝉′𝒊 and the joint torque limitations 𝝉𝒊,𝒎𝒂𝒙 . The sum of
the individual manipulators’ task capabilities provides the group’s total capability 𝐾 =∑ 𝑘𝑖 , where 𝐾 is the scaling parameter of the total task 𝒉𝒐 . The individual manipulators
share the task proportional to their task capabilities 𝑘𝑖 obtained using efficient utilization of a manipulator. Dynamic task allocation coefficient 𝛽𝑖 = 𝑘𝑖 ⁄𝐾 . The task shareby 𝑖 − 𝑡ℎ manipulator for the task would be 𝛽𝑖 𝒉𝒐 .
max 𝑘𝑖𝑠. 𝑡. |𝝉′𝑖 + 𝑘𝑖 𝑱𝑻𝒊 (𝒒)𝒉𝒐 | ≤ 𝝉𝑖,𝑚𝑎𝑥
𝑘𝑖 > 0(1)

69

Fig. 1 (a) The task capability of the three manipulator arms 𝑘1 , 𝑘2 , 𝑘3 and the total
task capability 𝐾, (b) 2-D path tracing by the center of mass of the manipulated object,and (c) Trajectory tracking performances.
Numerical studies on three manipulators performing a task of trajectory tracking by theobject’s center of mass, indicate the efficacy. The diverging sinusoid-like trajectory[0.3 + 0.01𝑡 + 0.001𝑡 3 , 0,0.35 + 0.01𝑡𝑐𝑜𝑠(2𝜋𝑡)]𝑇 𝑚 is considered here. All EEs rigidly grasped the object on its periphery. The proposed method efficiently computes
online task capabilities 85% faster than the existing vertex search-based state-of-art
capability finding algorithm [4] and dynamically allocates the task for efficient utilization of the capability. The trajectory tracking performance in Fig. 1 shows the efficacy of the proposed metric. Near 𝑡 = 2.5 𝑠𝑒𝑐 (Fig. 1. (a)) when the value of 𝐾 (0.93)
goes below one the trajectory tracking performance deteriorated, evidenced by Fig.1(c). For successful task completion, the total capability (𝐾) should be greater than one
at every instant. The trend of trajectory tracking error matches with the predictions of
the proposed metric. The task capability aids in identifying the least capable manipulator for the task. Identifying such a least capable one amongst a group of manipulators
assists in the efficient utilization of the capability of the group.

References
1. Chiacchio P, Chiaverini S, Sciavicco L, Siciliano B (1991) Task space dynamic analysis ofmultiarm system configurations. The International Journal of Robotics Research 10(6):708–
715
2. Mejia L, Simas H, Martins D (2015) Force capability in general 3dof planar mechanisms.
Mechanism and Machine Theory 91:120–134
3. Sheng Zhao Y, Lu L, Shi Zhao T, Hui Du Y, Huang Z (1999) The novel approaches forcomputing the dynamic load-carrying capacity of multiple cooperating robotic manipulators.
Mechanism and Machine Theory 34(4):637–643
4. Skuric A, Padois V, Daney D (2021) On-line force capability evaluation based on efficient
polytope vertex search. In: 2021 IEEE International Conference on Robotics and Automation (ICRA), pp 1700–1706, DOI 10.1109/ICRA48506.2021.95620
5. Yoshikawa T (1985) Manipulability of robotic mechanisms. The International Journal of
Robotics Research 4:3–970

Experimental research of a parallel manipulator in asingular configuration
Jacek Bałchanowski[0000-0002-1510-0122] and Sławomir Wudarczyk[0000-0003-4953-4516]
1 Wrocław University of Science and Technology, Wrocław, Poland
jacek.balchanowski@pwr.edu.pl,slawomir.wudarczyk@pwr.edu.pl

1

Materials and methods

Mechanism links can assume kinematically indeterminate positions during operation. Such positions of the mechanism are commonly called singularity configurations.
A system brought to such a configuration changes its kinematic and dynamic properties.
Singular configurations of parallel manipulators are configurations at which the robot
loses its natural rigidity. At these configurations, one or more degrees of freedom of theplatform become uncontrollable [2, 4, 5].
A 3RUU parallel manipulator with 3 DoF near a singular position described by anangle q(0) = 27.65o was subjected to stand tests (Fig. 1). The singular configurations of
this system were determined analytically [1, 3].

Fig. 1. View of the 3RUU manipulator in the analyzed singular configuration

The experimental study measured the platform's positioning accuracy near the singularconfiguration depending on the qi drive settings. The tests consisted of placing the manipulator in the qi measurement position and measuring the deflection uz of platform
under the load of the force Fi caused by the mass mi. The scheme of the experiment andmeasurements is shown in Fig. 2.

Fig. 2. Views of the stand and diagram of how to carry out the measurements of the deflectionof the manipulator platform: a) unloaded platform, b) loaded platform

The tests were conducted in the range q(0) ≤ qi ≤ 90o. Measurements were made forthree different loads on the platform with forces F1 = 14.70 N, F2 = 29.40 N,

71

F3 = 75.50 N. Analyzing the results, it can be seen that as the platform approaches the
singular position q(0), the values of uz deflection increase significantly, and from a specific value, they change abruptly (Figure 3). This indicates that the system in the singular position rapidly loses stiffness.

Fig. 3. Deflections of uz center of the platform under load Fi as a function of rotation angle qi

Measurements have shown that it can also be dangerous for the mechanism's links
to approach the singular configuration. A system loaded with a higher force enters the
singular position sooner. The entry point into the singularity can be read from the diagrams of the deflection of uz at the points of abrupt changes in the waveforms.

2

Final Remarks

The obtained experimental results of the manipulator indicate that it is impossible toobtain influence on holding the set position of the links in the singular configuration.
Hence, when planning working trajectories, it is necessary not only not to bring thesystem into the singularity, but also to maintain an appropriate "safe distance" fromsingular configurations. The results of the experiments and measurements confirm thetheoretical conditions for the categorical prohibition of introducing of parallel manipulators into singular configurations from the task of direct kinematics. This conditions
the development of such drive control algorithms to prevent the execution of trajectories leading to singular positions.

References
1. Bałchanowski J.: Topology and analysis of the singularities of a parallel mechanism withthree degrees of freedom. Archives of Civil and Mechanical Engineering. vol. 14, 80–87,(2014).
2. Bałchanowski J.: Spatial parallel mechanisms. Analysis and Synthesis. Publishing House of
Wrocław University of Science and Technology, Wrocław, Poland (in Polish), (2016).
3. Bałchanowski J., Szrek J., Wudarczyk J.: Analysis of constraint equations of the parallelmechanisms with 3 DoF in singular configurations. Proceedings of the 15th IFToMM World
Congress on Mechanism and Machine Science, Springer, 607-616, (2019).
4. Gosselin C., J. Angeles J., Singularity analysis of closed-loop kinematic chains, IEEE Trans.
Robot. Automat., vol. 6, 281–290, (1990).
5. J.-P. Merlet J. -P: Parallel Robots. Springer Dordrecht, ISBN 978-1-4020-4132-7, (2006).

72

Design of Underwater Robot system for collecting
Floating debris
Sangheon Roh1[0009-0009-6136-5760] , Donghwi Shin1[0009-0005-5121-947X], Jeonghyeon
Lee2[0009-0000-2758-6273], Taegyun Kim#1[0000-0002-7655-1883] and Sungkeun Lee#2[0000-0002-53932560]
1 Yeungnam University, Gyeonsan-si, Republic of Korea
2 Keimyung University, dalseo-gu, Republic of Korea#1 Yeungnam University, Gyeonsan-si, Republic of Korea

tgkim@yu.ac.kr#2 Keimyung University, dalseo-gu, Republic of Korea

skyoo@kmu.ac.kr

Abstract. This paper presents a system design for an underwater robot capableof collecting floating debris on the water's surface using pumps and a vortex
generator. An experimental environment was established, and a series of experiments were conducted to confirm the performance of the vortex generator withvarying parameters, including pump pressure, vortex generator angle, motor
control for vortex generation, and the vortex inlet shape. The optimal design
criterion for the underwater robot was the power consumption during operationand the speed of the floating object induced by the generated vortex, measured
using vision-based methods. An experiment was conducted to determine the optimal design value of the underwater robot system. Data to establish the relationship between various design criteria and vortex performance were obtained
through various experiments. In this process, the suction mechanism of the vortex generator was optimized. The proposed system provides an effective solution for collecting floating debris on the water's surface.

Keywords: Underwater robot, Vortex generator, Floating debris, computer vision

1

Introduction

The environmental impact is increasing due to the rise in floating waste in rivers andseas. To mitigate environmental problems, it is necessary to reduce the amount offloating waste. However, floating debris often exists in various environments andlocations that are difficult for humans to access. As the vortex generated in the water
has the property of collecting floating matter in the center, it can effectively collectfloating waste over a large area proportional to the size of the vortex. This paper introduces an underwater robot that utilizes a vortex to collect floating waste around it.

73

2

Hardware Design

2.1

Overall Structure of underwater robot and testbench

Fig. 1(a) shows a load cell that measures the change in buoyancy, and a motor for therotation mechanism that measures the input power. The flow sensor measures thepump discharge flow rate, and the discharge pump measures the pump input power.
Fig. 1(b) shows a vision system for obtaining the speed of floating matter in the vortex. Fig. 1(c) shows the structure of the vortex generator, which includes a flow dispersion device that helps maintain the shape of the vortex.

Fig. 1. (a) Various sensors. (b) Vision system. (c) Vortex generator.

References
1. Suaria, G., & Aliani, S. (2014). Floating debris in the Mediterranean Sea. Marine pollution
bulletin, 86(1-2), 494-504.
2. Xie, Q., Wang, T., Yao, S., Zhu, Z., Tan, N., & Zhu, S. (2020). Design and modeling of ahydraulic soft actuator with three degrees of freedom. Smart Materials and Structures, 29(12), 125017.
3. Youngtak Kim, Function, Computational Thinking and Python Programing, 1th ed,
HONGREUNG, PUBLISHING COMPANY, Korea(2022)

Acknowledgement
This research was supported by Basic Science Research Program through the National
Research Foundation of Korea(NRF) funded by the Ministry of Education(No. NRF2022R1I1A3072904)

74

Robust Position Control Through Variable Stiffness andDamping
DongHwi Shin 1[0009-0005-5121-947X], MinNo Lee 1[0009-0002-6493-5617], SangHeon Roh 1[00090009-6136-5760] and TaeGyun Kim #[0000-0002-7655-1883]
1#

Yeungnam Univ, 280, Daehak-ro, Gyeongsan-si, Gyeongsangbuk-do, Republic of Korea
Yeungnam Univ, 280, Daehak-ro, Gyeongsan-si, Gyeongsangbuk-do, Republic of Korea
tgkim@yu.ac.kr

Abstract. This paper presents a 1-degree-of-freedom system with a variable stiffness and variable-damping mechanism utilizing one pair of springs and rubber
friction. A wide range of target impedance can be achieved, and the overall system consumes less energy due to the presented mechanism. The dynamic model
was defined and validated through simulation and real-world experiments. Results show that the damping coefficient is a function of contact force, contact
area, and material, while the stiffness of system, which is nonlinear, depends oneach of the three motor angles. To simplify impedance control, the non-linear
term was linearized by the Stiffness-Controller that controls the two springmounted motors separately to follow a reference spring constant. The ultimate
goal of the study is to achieve robust position control using impedance control ina disturbance environment. Overall, the paper presents an approach to designinga system with variable stiffness and damping that could be useful in various adaptive control applications, such as polishing and grinding robots.
Keywords: Variable stiffness, Variable damping, Impedance control, Robustposition control.

1Introduction

In the manufacturing process, polishing is a kind of finishing process to obtain evensurface condition. In generally, most of the surface subject to polishing has high stiffness and same for the machine. Improper contact force can damage both the surface
and the machine in this condition. For a good surface condition (low surface roughness), it is important to finely follow reference force in terms of force control. Also
Reducing external influence like vibration should be considered. Therefore, we proposea system with adjustable impedance not only virtually but also mechanically.

2

Design of Hardware

The presented system uses four motors. Two for variable stiffness, rest of them usedfor variable damping and main rotor respectively. One pair of springs are connected75

between main rotor and each of two motors. For damping, rubber pad is mounted in
front of loadcell and this part can move up and down to make friction on main rotor.
This hardware can change its stiffness and damping roughly but for more precision,
impedance control in main rotor should control rest of it.

3

Dynamic Analysis

There are three controllers below. Each controller is responsible for generate corresponding torque such as damping, stiffness and impedance torque to main rotor.
∑ 𝑀𝑀𝑜𝑜 = 𝐽𝐽𝑚𝑚 𝜃𝜃̈ = Damping CONT (𝐷𝐷𝑚𝑚 ) + Stiffness CONT(𝐾𝐾𝑚𝑚 ) +𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼 CONT(𝐽𝐽𝑐𝑐 ,𝐷𝐷𝑐𝑐 , 𝐾𝐾𝑐𝑐 )𝐽𝐽𝑚𝑚 𝜃𝜃̈ = −𝐾𝐾𝑚𝑚 𝜃𝜃 − 𝐷𝐷𝑚𝑚 𝜃𝜃̇ + (𝐽𝐽𝑐𝑐 𝜃𝜃̈ + 𝐷𝐷𝑐𝑐 𝜃𝜃̇ + 𝐾𝐾𝑐𝑐 𝜃𝜃)(𝐽𝐽𝑚𝑚 − 𝐽𝐽𝑐𝑐 )𝜃𝜃̈ + (𝐷𝐷𝑚𝑚 − 𝐷𝐷𝑐𝑐 )𝜃𝜃̇ + (𝐾𝐾𝑚𝑚 − 𝐾𝐾𝑐𝑐 )𝜃𝜃 = 0

(1)
(2)
(3)

Fig. 1. 1-degree-of-freedom system for Robust position control.

References
1. Laffranchi, M ., Tsagarakis, N. G., & Caldwell, D. G. (2010, M ay). A variable physicaldamping actuator (VPDA) for compliant robotic joints. In 2010 IEEE International Conference on Robotics and Automation (pp. 1668-1674). IEEE.
2. Sarakoglou, I., Tsagarakis, N. G., & Caldwell, D. G. (2014, M ay). Development of a hybrid
actuator with controllable mechanical damping. In 2014 IEEE International Conference on
Robotics and Automation (ICRA) (pp. 1078-1083). IEEE.
3. Radulescu, A., Howard, M ., Braun, D. J., & Vijayakumar, S. (2012, July). Exploiting variable physical damping in rapid movement tasks. In 2012 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM) (pp. 141-148). IEEE.

Acknowledgement
This research was supported by Basic Science Research Program through the National
Research Foundation of Korea(NRF) funded by the Ministry of Education(No. NRF2021R1I1A 3059727)

76

Unfolded Paper Manipulation by a Robot Hand
Using High-speed Image Processing
Hideto Okura1 , Shunsuke Komizunai2 , Taku Senoo1 , and Atsushi Konno1
11

Graduate school of Information Science and Technology, Hokkaido University,
Sapporo, Japan,{okura@scc,senoo@ssi,konno@ssi}.ist.hokudai.ac.jp,
2
Faculty of Engineering and Design, Kagawa University, Takamatsu, Japan

Introduction

Nowadays, handling paper is an essential part of everyday life and is requiredin various situations. Since paper is a ﬂexible material, its stiﬀness changes
irregularly when folded. Therefore, precise handling requires bending withoutcreases. Examples of such tasks include handling and transferring paper, as wellas packaging work. Although the several studies on paper grasping have beenreported [1], [2], its manipulation was static and slow. Causes of diﬃculties inmanipulating ﬂexible objects include deformation of the ﬂexible object during
manipulation and estimating the amount of deformation of the ﬂexible object.
The goal of this study is to solve the diﬃculty of ﬂexible object manipulation by
combining a multi-ﬁnger robotic hand with visual information from high-speed
vision, and to manipulate paper as if it were a human hand. By dynamicallymanipulating paper, it performs the task of changing paper from a gravitationally bent state to a taut state with a small number of degrees of freedom and athigh speed.

2

Proposed Method

Paper has the property of having stiﬀness in the direction perpendicular to thedirection of bending. A smooth curved surface that can be created simply bybending a sheet of paper without incising or creasing it is called a ﬂexible surface,and has the property that at any given point, a straight line passing throughthat point exists on the curved surface. In other words, the shape of paper canbe manipulated by applying a bending force in a direction perpendicular to thedesired bending direction.
In this study, a high-speed vision system is used to detect paper deformations
in real time. Due to the nature of perspective projection, the contours of thepaper captured by the camera are distorted in the direction of the curved surface.
This distortion is calculated by cubic spline interpolation of four markers placed
at equal intervals on each side of the paper. The curvature of the resulting curves
is calculated to provide feedback on how much the paper is bent. The markers
are tracked using a self-windowing method that takes advantage of the propertiesof high-speed vision. This process achieved a high processing speed of 300 Hz.

77

Fig. 1: Manipulation of the paper shapes using both hands

Fig. 2: Manipulation of the paper shapes using one hand3

ResultFigure 1 shows how the paper shape is manipulated by applying force from bothsides. Since only one hand was available for this study, the paper shape wasmanipulated by ﬁxing one side of the hand to reproduce a two-handed grasp.
Figure 2 shows a piece of paper being grasped by a robot hand. The paper canbe manipulated dynamically and at high speed by deforming the shape of thepaper surface using the inertia caused by the downward swing of the hand. By
devising manipulation operations and applying image processing to detect theshape of the paper surface even during high-speed movements, the appropriate
timing for switching operations could be obtained. As a result, the paper surface
can be manipulated and constrained quickly and with minimal movement.

4

Conclusion

This paper proposes a handling strategy that can impart stiﬀness in any direction
by exploiting the physical properties of paper. By optimizing the procedure ofmanipulating paper using this strategy, it became possible to perform dynamic
bending operations of paper without making creases. In the future, eﬀorts will
be made to achieve more complex movements by increasing degrees of freedom
using a robot arm.

References
1. K, Hoya., et al.: On Grasping a Sheet of Paper by Multi-Fingered Hand, SICE
Tohoku Chapter, Vol. 293(2015), No. 7. (in Japanese)
2. C, Elbrechter., et al.: Bi-Manual Robotic Paper Manipulation Based on Real-Time
Maker Tracking and Physical Modelling. In: IEEE/RSJ International Conferenceon Intelligent Robots and Systems, pp. 1427–1432. (2001).

78

Tactile determination of the instantaneous screw
axis of a human knee surrogate by aforce-controlled robot using a Krylov method
Alexander Hoffmann, Patrick Jendro, and Andrés Kecskeméthy
Universität Duisburg-Essen, Duisburg, Germany,
alexander.hoffmann-lmr@uni-due.de,
WWW home page: https://www.uni-due.de/mechanikb/

Knowledge about human joint axis location and orientation is required forrehabilitation robotics and surgical planning procedures. An approach based ona tactile force-controlled robot is developed in [1], to which this paper presentsa follow-up stemming from a project to determine the instantaneous screw axis
(ISA) of a human knee (Fig. 1). A surrogate with a revolute joint (Fig. 2) isutilized for intermediate testing [2], while the traction boot requires no further
adaptations for future experiments. A force/moment sensor is mounted at theend-effector of the robot, which is coupled to the set-up to guide its movement.

IS

d

A

aISA

∆α

u

Pend

∆s

Pini

Fig. 1. Project vision

Fig. 2. Test set-up

Fig. 3. Inital and final pose

For ISA determination, the initial and final pose of an incremental movement in
direction of least resistance u are analyzed (Fig. 3). A power iteration method[1] is applied to iteratively determine the eigenvector of the greatest eigenvalueof the compliance matrix, which corresponds to the sought direction u. Then the
ISA orientation is derived from the end-effector rotation from initial to final poseexpressed by rotation axis aISA and angle ∆α. The ISA position dISA is determined by analyzing the isosceles triangle spanned in time by the step distance∆s and dISA at the initial and final end-effector pose. The robots movement
is controlled by a fully parallel force and torque admittance controller according to [3] combined with two low-pass filters LP (Fig. 4). In order to avoid theforce and moment control working against each other, a coupling of the two was
pre-installed in the force/moment control such that the desired moment at the
expected ISA due to the orthogonal force component is subtracted from the sen-79

sor moment. In this way, the control predicts an estimate of the correct rotation
about the current ISA, denoted as CISA . In the control scheme, the admittancecontroller determines the desired position and orientation of the end-effector,
which are transformed by inverse kinematics for the inner position control loopof the manipulator realized in joint space. The measured force F m and moment τ m are fed back to the admittance controller. The control law with force
difference ∆F = F d − F m and moment difference ∆τ = τ d − τ m as inputs is   
 
∆F
MT
DT
r̈
ṙ
=
+
(1)
∆τ
ω̇
ω
MR
DR
where r and ω denote the position and angular velocity increments respectively.
The diagonal positive 3×3 matrices M and D represent virtual translational (T )and rotational (R) mass and damping matrix respectively. Experimentally a
trajectory guidance with mean deviations of 1.0073 mm and four checkpoints leadto an orientation error of 2.8057◦ and a positioning error of 0.6997 mm on averagein identifying the ISA (Fig. 5). Future research will focus on validating the
proposed algorithm with artificial knees and human limbs as project objectives.

Fdτ d LP

LP
CISA

CL

rd

R

R

Rd

Fig. 4. Admittance control scheme

Fig. 5. Resulting trajectory

Public funding acknowledgment
This research was partially funded by the German Federal Ministry of Education
and Research under support code 16SV8516. The authors thank Battenberg
Robotic GmbH & Co. KG for cooperation in experiment design and execution.

References
1. Liu, H., Kecskeméthy, A., Nguyen, D.H., Parzer, H., Gattringer, H.: Determinationof an unknown unactuated joint axis in a compliant serial kinematical chain using force control and the Krylov power iteration method. Mechanism and Machine
Theory. 2017. vol. 117. pp. 198-209.
2. Lohse, N.: Entwicklung eines Beinmodells mit anschließender Messung und Analysevon mechanischen Kenngrößen bei der robotergestützten Kniegelenkanalyse (unpublished master’s thesis). Justus-Liebig-Universität Giessen. 2021.
3. Siciliano, B., Villani, L.: Robot Force Control. Kluwer Academic Publishers. 1999.

80

Design of a hybrid suspended cable and thruster
driven parallel robot using hexarotor
Yifan Feng1 , Yusuke Sugahara1 , Ming Jiang1 , Marco Ceccarelli2,3 , and Yukio
Takeda1
1
Tokyo Institute of Technology, Tokyo, Japan{ho.i.aa, sugahara.y.ab, jiang.m.ad, takeda.y.aa}@m.titech.ac.jp,
2International Research Frontiers Initiative, School of Engineering, Tokyo Instituteof Technology, Tokyo, Japan
3
University of Rome Tor Vergata, Rome, Italy
marco.ceccarelli@uniroma2.it

Cable-driven parallel robots (CDPRs) have been studied for decades for thecapability of high speed and acceleration motion over a wide workspace with low
inertia. However, due to the characteristic that cable can only pull but not push,at least n+1 cables are required to fully control the n degrees-of-freedom (DOF)of the end-effector(EE). The set of feasible EE poses can be collectively referred
to as the wrench-feasible workspace (WFW) [1]. Adding extra cables can expand
the WFW, but it decreases the interference-free workspace (IFW), especiallywhen there are collisions between the cables under the EE and obstacles on
the ground. Cable-suspended parallel robots (CSPRs) do not have cables below,
but the cable tension depends on the gravitational force acting on the EE. A
lightweight EE reduces the WFW, while a heavy one compromises accelerationand safety.
Recent developments in unmanned aerial vehicles (UAVs) have inspired theuse of thrusters in CDPRs. Thrusters can offer greater flexibility for generating
additional wrenches that can be freely attached on EE. Furthermore, the addition of thrusters has minimal impact on IFW. In [2], co-axial counter-rotating
propellers as thrusters are utilized to generate unidirectional forces and counteract the effects of gyroscopic moments, and the arrangement of thrusters on the
EE to generate a desired wrench set within a specified workspace.
CDPRs have potential advantages for use in indoor collaborative robotics
with the function of such as picking, placing, and transporting items that require a specific orientation. If it is intended to be used in a confined room withlimited overall structure space, the maximum distance between the winches connecting one end of the cable is restricted. Therefore the propellers as thrusters
can be applied to enhance the WFW and IFW, and considering the effects ofdirections, connection positions, maximum thrust of propellers, a fully actuatedhexarotor is employed, as shown in Figure 1, which is able to decouple position
and attitude control. The fully actuated hexarotor fixed on the EE that is reversal facing downward is proposed, which is shown in Figure 2. Three cables
connect winches and EE, generating three-dimensional forces, but there is no
downward component. The hexarotor generates three-dimensional torques thatare used to control the attitude of the EE, as well as three-dimensional forces.

81

The vertical downward force is applied to maintain tension in the cables, while
the horizontal force is used to further expand the WFW.

Fig. 1. Schematic diagram of fully actu- Fig. 2. Schematic diagram of CSPR withated hexarotor with double-tilted rotors fully actuated hexarotor

Hyperplane Shifting Method proposed in [3] is used to calculate the WFW.
Since the hexarotor independently controls the attitude of the EE, only the 3
DOF translational motion is considered in this calculation. WFW is indicated by
the colored dots in Figures 3, and can be significantly expanded by increasing thethrust in a single downward direction. Figure 4 demonstrates that the WFW canbe further expanded by employing the hexarotor arrangement and distributing
a total force of 90 N to each of the six propellers.

Fig. 3. CSPR with unidirectional downward 30 N & 90 N thrust and the WFW Fig. 4. CSPR with hexarotor and theare 2 m3 (Blue) & 6.22 m3 (Blue and Red) WFW is 7.98 m3

References
1. Abbasnejad, G., Eden, J., & Lau, D. (2018). Generalized ray-based lattice generationand graph representation of wrench-closure workspace for arbitrary cable-driven
robots. IEEE Transactions on Robotics, 35(1), 147-161.
2. Sun, Y., Guo, Y., Song, C., & Lau, D. (2022). Wrench-feasible workspace-based
design of hybrid thruster and cable driven parallel robots. Mechanism and Machine
Theory, 172, 104758.
3. Bouchard, S., Ement, C., Gosselin, C., & Moore, B. (2010). On the ability of acable-driven robot to generate a prescribed set of wrenches. Journal of Mechanisms
and Robotics, 2, 1-9.

82

Machine Learning Aided Self-Calibration Schemes for
Parallel Kinematic Manipulators
Yu-Jen Chiu1*, Wei-Hsuan Lin2, Cheng-Kuo Sung2 and Syanala Jaya Prakash Reddy1
1 Ming Chi University of Technology, New Taipei City 243303, Taiwan R.O.C.
2 National Tsing Hua University, Hsinchu 300044, Taiwan R.O.C.

yjchiu@mail.mcut.edu.tw

1

Introduction

Self-calibration or autonomous calibration methods have been well-known for compensating kinematic errors in the robotics areas for the recent decades. The methods
require no expensive metrology equipment and avoid the measurement procedures thatare time consuming, inconvenient, and difficult to obtain accurate results. Indeed, there
inevitably exist certain limitations, such as the issues of redundant parameters, observability of the selected postures, the complexity of the error models [1]. Self-calibration
schemes have been approved to be feasible and effective due to their benefits. The conventional calibration is based on the analytical error models, thus is generally dealing
with the geometrical error sources. Researchers have been devoting themselves into theinvestigation of the machine learning algorithms for calibrating non-geometrical errors.
Nonetheless, massive measurement by individual equipment is essential for training amachine learning model. The present work is aimed at the possibilities that a self-calibration approach incorporates machine learning algorithms to enhance the positioning
accuracy of a parallel kinematic manipulator (PKM).

2

Methods

A translational 3-UPU configured PKM with variable-length links is considered as anillustrative example. Each of the three links of the PKM is dismantled into two universal
joints Ai, Bi and one extensible link Li (i = 1, 2, 3). In addition to the encoders on thedriving motors to control the lengths of the links, there are additional 6 redundant sensors installed on each passive joint Ai and Bi (Fig. 1). The objective of the conventional
calibration method is to identify the parameters in the kinematic error model. Theoretically, only one redundant sensor is capable of fulfilling self-calibration purposes. In
the neural network (NN) methods, the compensation values of the actuating variables
are pursued alternatively [2]. In this work, the position errors of all joints and the detected offsets of all sensors are considered. The compensation values of the link lengths
 Li and the angular deviation of the redundant sensor readings i and i are introduced. For each real posture, various estimated postures Xj can be obtained according
to different kinematic chains j and the sensor readings Li   Li , i  i and i  i
within the PKM. The genetic algorithm is adopted for searching the best fit of  Li ,i and i such that the estimated posture errors from different kinematic chains areminimized. Based on a number of postures, the combinations of X j (input) andLi   Li (output) are achieved to serve as the basis for NN training. The resultant NN
function therefore provides the actuated variables for the desired postures.

83

3

Results and Discussion

For the self-calibration schemes based on the kinematic error models, 17 kinematicparameters are identified by adopting 6 redundant sensors and 3 positions for data acquisition. The translational and angular errors for joint locations and sensor readings
are within the range of 1 mm and 0.5 , respectively. Figure 2(a) reveals the resultant trajectories of a circular path are accurately improved. The root mean squares error
is significantly reduced from 2.16 mm to 2.63  105 mm in the simulation. As for theneural network approach, another 100 positions of the end-effector are randomly generated within the feasible workspace. The translational and angular errors for joint locations and sensor readings are introduced within the range of 0.2 mm and 0.5 ,respectively. The neural network aided self-calibration scheme reduces root meansquares error of the positioning accuracy from 1.450 (un-calibrated) to 1.321 mm. The
error reduction rate in Fig. 2(b) shows an obvious tendency to enhance the positioning
accuracy (below the red line), nonetheless, some tests become worse in the illustrative
example. It reveals certain limitation worthy of further investigations.

Fig. 1. A 3-UPU type PKM and the installation of redundant sensors.

(a)(b)
Fig. 2. The improvement in the positioning accuracy: (a)the self-calibration schemes based onkinematic error models; (b)the effectiveness of the neural network aided self-calibration scheme.

Acknowledgement
This work was financially supported by the National Science and Technology Council,
Taiwan, R.O.C. (NSTC 111-2221-E-007-068-MY2 and NSTC 112-2637-E-131-005).

References
1. Chiu, Y. J. and Perng, M. H.: Self-calibration of a general hexapod manipulator with enhanced precision in 5-DOF motions. Mechanism and Machine Theory 39(1), 1–23 (2004).
2. Zhong, X., Lewis J. and N-Nagy F. L.: Inverse robot calibration using artificial neural networks. Engineering Applications of Artificial Intelligence (9), 83–93 (1996).

84

Foldable base plate mechanism for parallel link robots
Daigo Tokunaga1[0009-0009-4191-7521], Satoshi Nishikawa1[0000-0003-0905-8615]
and Kazuo Kiguchi1[0000-0003-4408-0420]
1 Kyushu University, Fukuoka, 819–0395, Japan

kiguchi@ieee.org

1

Introduction

Robotic limbs have been studied in a great number of configurations, some mimicking living organisms and others specialized to perform a desired function [1]. Parallel
link manipulators are used to develop robotic limbs that exhibit high rigidity [2][3].
However, most parallel link mechanisms have actuators located near the base plate, andthe base plate also becomes larger when the actuator size increases according to therequired output characteristics. Some robots use a wide base plate to ensure that theactuators have a range of motion without interfering with each other. When robots areapplied to support human behavior in living environments, it is desirable for the robots
to change their size to be suitable for the desired workload and space. Therefore, aparallel link robot that can change the size of its base plate, which is the largest part ofthe parallel link robot, is proposed.

2

Foldable base plate mechanism

The robotic limb shown in Fig. 1(a) is taken as an example of the parallel link robot
in which the proposed foldable base plate mechanism is applied. The robotic limb canchange the characteristics of the end-effector's output and range of motion by manipulating the force point and pivot point of the lever mechanism with two 3-sphericalprismatic-revolute parallel manipulators [4]. Fig. 1(b)(c)(d) shows a 3D model of the
proposed foldable base plate mechanism. Each actuator mounting point is connected tothe circle plate via vertical links, horizontal link and hexagonal plates. Vertical links
are driven by a ball screw in the center, and actuator mounting points move linearly
from the center. The hexagonal plate rotates around the central circle plate to which theball screw is attached. The Pitch Circle Diameter (PCD) of the actuator mounting position in Fig. 1 is 360 mm in the open position and 190 mm in the closed position,
reproducing the PCD of the existing base plate. The range of PCD is determined by thelength of the link arm and the link ratio. In the closed position, the end-effector can
only move vertically with respect to the base. The base can be continuously expanded,
and as the distance of expansion increases, the range of motion of the robotic limb
increases as well as the rigidity against moments applied to the end-effector (Fig.2).
*This work was supported by JST [Moonshot R&D][Grant Number JPMJMS2034].

85

Fig. 1. The robotic limb and the proposed base structure. (a) The robotic limb using an adjustablelever mechanism with double parallel link platforms. (b) The mechanism of one actuator. (c)(d)The mechanism changes continuously from state (c) to state (d).

Fig. 2. Maximum output force profiles at the end-effector when actuator mounting PCD is 200,
280, and 360mm. The thrust of each actuator in this simulation is 1500 N.

References
1. X. Zhou and S. Bi, “A survey of bio-inspired compliant legged robot designs,” Bioinspiration & biomimetics, vol. 7, no. 4, p. 041001 (2012).
2. P. Yang and F. Gao, “Leg kinematic analysis and prototype experiments of walking-operating multifunctional hexapod robot,” Proceedings of the Institution of Mechanical Engineers,
Part C: Journal of Mechanical Engineering Science, vol. 228, no. 12, pp. 2217–2232 (2014).
3. M. Morisawa, T. Yakoh, T. Murakami, and K. Ohnishi, “A comparison study between parallel and serial linked structures in biped robot system,” in 26th Annual Conference of theIEEE Industrial Electronics Society (IECON), vol. 4, pp. 2614–2619. (2000).
4. S. Nishikawa, D. Tokunaga and K. Kiguchi, "Adjustable Lever Mechanism with Double
Parallel Link Platforms for Robotic Limbs," IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Kyoto, Japan, pp. 1950-1956 (2022).

86Vibration isolation in spacecraft using Gough-Stewart
Platform
Yogesh Pratap Singh1[0000−0001−6582−6004] and Ashitava Ghosal1[0000−0002−8308−7724]
1 Indian Institute of Science, Bangalore 560012, India{yogeshsingh,asitava}@iisc.ac.in

1

Introduction

In spacecraft, micro-vibrations (up to 300 Hertz) induced due to the presence of reaction wheels, momentum wheels, and cryocoolers, reduces the pointing accuracy ofsensitive payloads mounted on it. A 6 degree of freedom Gough-Stewart platform(GSP) is effective for isolating payloads from these micro-vibrations. It is known thata conventional Gough- Stewart platform fails to give dynamic isotropy where the firstsix vibration modes have the same or nearly the same natural frequency. The primaryreasons to use dynamically isotropic GSP are a) it is easy to tune dampers for passive
vibration attenuation for the given frequency bandwidth, and b) a multi-input-multioutput system system can be treated as six decoupled single-input-multi-output systems (for six degrees of freedom), which simplifies active control.
A two radii or Modified Gough-Stewart Platform (MGSP) is proposed toachieve dynamic isotropy. An MGSP is a parallel manipulator with a movable top
platform, a fixed base, and struts with a linear actuator in between them. It differsfrom the traditional GSP with the anchoring points/spherical joints are on two radii oneach platform instead of on one radius in a traditional GSP, as shown in Fig. 1(a). In
an MGSP, these struts are divided into two sets having a rotational symmetry for their
attachment points along the circumference with an equal angular spacing of 120°.

2

Design of MGSPThe unknowns (design parameters) for an MGSP are the inner and outer radii ofthe bottom and top platforms, 𝑅𝑏𝑖 , 𝑅𝑡𝑖 , 𝑅𝑏𝑜 , 𝑅𝑡𝑜 the angular separation of the connection points in the top and bottom platform (inner and outer), 𝛼𝑡𝑜 , (𝛼𝑏𝑖 − 𝛼𝑡𝑖 ), the leg
length ratio 𝑎, and the height of the top platform 𝐻 from the bottom platform (seeFig. 1a). The force transformation matrix ([𝐁]), together with a novel geometry-based
approach, is used to obtain closed-form analytical solutions in their explicit form for
dynamic isotropy in a 6-6 MGSP at its neutral position. For dynamic isotropy, the six
eigenvalues of the natural frequency matrix [𝐆] [1] must be equal.
[𝐆] = [𝐌]−1 [𝐊 𝐓 ] = [𝐌]−1 𝑘[𝐁][𝑩]𝑇(1)

where [𝐌] is the mass matrix of the payload, [𝐊 𝐓 ] is the stiffness matrix in the task

87

Fig. 1. a) MGSP, b) Geometrical interpretation of MGSPs’ design variables [1]space, and k is the axial stiffness of each strut. The obtained set of transcendental
equations from equal eigenvalue conditions lead to several geometrical observations
from where closed-form solutions to the design variables were developed [1] – a 3-D
dynamically isotropic MGSP design problem could be simplified into sets of triangles
in 2-D space related by certain geometrical relationships (refer to Fig. 1(b)) that canbe used to find the design variables.

3

Validation via simulation and experiments

A prototype based on flexural joints (refer to Fig. 2) was developed for experimentation (to avoid friction and backlash in the spherical joints), and various flexural
joints were explored before arriving at the final design. All six natural frequencies
obtained analytically from Section 2 match well with simulation results -- validating
our design. We were able to capture the first six modes experimentally lying in a narrow frequency bandwidth around 29 Hertz, which were very close to analytical andsimulation results. The platform is designed for approximately 10.5 Kg payload including the mobile platform and can isolate micro vibration above 41 Hertz.

Fig. 2. a) Various flexural joints explored, b) CAD model, c) Experiment prototype of MGSP

References
1. Singh, Y.P., Ghosal, A.: Dynamically isotropic Gough-Stewart platform design using apair of triangles. In: Proc. of 32nd International Conference on Robotics in Alpe-AdriaDanube Region, Springer Nature, Bled, Slovenia (2023, Accepted).

88Motion Design for Robotic Contact: Insertion
Tasks
Siamak Arbatani1 and József Kövecses1 Marek Teichmann2
1

Department of Mechanical Engineering and Centre for Intelligent Machines, McGill
University, Montréal, QC H3A 0C3, Canada,siamak.arbatani@mcgill.ca; jozsef.kovecses@mcgill.ca
2
CM Labs Simulations, Montréal, QC H3C 1T2, Canada
marek@cm-labs.com

Motion planning and trajectory tracking control for general unconstrained
motion of robotic arms is quite well-established and possible to achieve in different ways. On the other hand, motion while the robotic arm is in contact withstatic or dynamic objects is a much more complex problem to deal with.
In this work, we specifically study insertion tasks where a given motion of
the end effector is required but with the presence of contact. Such physical interactions can occur in both grasping and insertion and represent significant
challenges in various areas of robotic mechanical systems. Robotic motion tasks
with insertion can be challenging for conventional feedback control that is designed for free space trajectory tracking, and it may have to be augmented withforce feedback based control. A small misalignment between the insertion tooland socket can lead to unwanted phenomena such as jamming during an insertion
maneuver as a result of emerging contact forces.
Various approaches have been developed for motion planning and controlling
robotic systems which involve contact tasks. Established control methods withcompliant manipulators and mating parts require sophisticated and task specificdesigns as well as accurate models embedded in the control system along withmanually tuned feedback controllers to achieve acceptable performance.
Reinforcement Learning (RL) has shown strong potential in some challenging
applications. In RL based methods, human insight and intuition are replaced byautonomous learning techniques to achieve optimal control policy from exploring and exploiting the learning environment. Deep RL is successfully used inlearning of robotic navigation and manipulation skills [1]. Robotic contact tasks
are also examined with RL based methods in various studies. Sparse rewards arecommon in robotic manipulation applications. Reward shaping is quite challenging to guide the learning agent in these applications. Use of demonstrations totackle the sparse reward problem is first proposed in [2], and simulation based
demonstrations and the use of reverse curriculum in robotic contact tasks havealso been explored. Training of a Deep RL agent has also been examined directly
on a real robotic insertion setup [3]. In the training environment, they consider
outputs of a force/torque sensor and rounded position values of the peg as theirobservation space and desired force components and orientation angles of thepeg as their discrete action space. They have defined the reward function basedon distance between the peg and target for the search phase and downward dis-89

placement for the insertion phase. They have demonstrated high success rate in
all cases with maximum initial position and angle errors of 1 mm and 1 deg.
The majority of published work about RL-based robotic contact tasks use reward functions based on notions of distance, vision and output from force/torquesensors. Distance and vision would not provide any insight about the forces resulted from contacts. The information solely from force/torque sensors would
not characterize the motion in presence of contact forces. Therefore, in presenceof contact forces, feedback from a combination of sources are typically employed.
In this work, we investigate robotic contact maneuvers related to insertion
problems using a novel method that requires minimum information and employsa physically motivated reward function. We propose and develop a framework using reinforcement learning, specifically employing residual policy learning (RPL),
to tackle the problem.
The proposed approach augments the parametric robotic models, in our casean inverse kinematic model, with a learned element. This captures the part thatcannot be described by parametric models, but it also takes advantage of theinformation already contained in the parametric model. In the core of this framework lies a reward function that is designed based on physical considerations,and captures the important phenomena in insertion in a physically meaningful
way. The use and implementation of this reward function requires a minimum
level of information and instrumentation from the robotic system.
This work can be used in different applications. In this paper, we demonstrate
it in the context of simulation and human-computer interaction. The other possible application is in physical robotic contact manipulation.
Our demonstration of the framework includes a virtual robotic contact testbed
and human-computer interaction. The results obtained illustrate the effectiveness of the proposed approach. Sensitivity and uncertainty in contact friction
and in misalignment due to the insertion angle are analyzed and incorporated.
The parameters representing these are randomized during the learning step inorder to generalize the solution.
Three different training scenarios are investigated. It is found that the wider
range of insertion angle and randomized friction coefficient during the training
leads to more intuitive motion behaviour from the residual policy. Results present
100% success with the residual policy for both the prescribed motion and humancontrolled cases.

References
1. Kahn, G., Villaflor, A., Ding, B., Abbeel, P. & Levine, S. Self-supervised deep
reinforcement learning with generalized computation graphs for robot navigation.
2018 IEEE International Conference On Robotics And Automation (ICRA). pp.
5129-5136 (2018)
2. Hester, T., Vecerik, M., Pietquin, O., Lanctot, M., Schaul, T., Piot, B., Horgan, D.,
Quan, J., Sendonaris, A., Osband, I. & Others Deep q-learning from demonstrations.
Proceedings Of The AAAI Conference On Artificial Intelligence. 32 (2018)
3. Inoue, T., De Magistris, G., Munawar, A., Yokoya, T. & Tachibana, R. Deep reinforcement learning for high precision assembly tasks. 2017 IEEE/RSJ International
Conference On Intelligent Robots And Systems (IROS). pp. 819-825 (2017)90

Optimal inverse kinematics solution for redundant
manipulators combined with trajectory scalingŁukasz Woliński1[0000-0001-9617-4117] and Marek Wojtyra1[0000-0001-7225-7647]
1 Warsaw University of Technology, IAAM, Nowowiejska Str. 24, 00-665 Warsaw, Poland

Marek.Wojtyra@pw.edu.pl

1

Introduction

A kinematically redundant structure increases the dexterity of the robotic manipulator
and offers an ability to avoid obstacles and handle singularities. Therefore, redundantrobots are well-suited for work in human-centered, cluttered environments. However,planning of the joint trajectory that satisfies the desired end effector trajectory and does
not exceed the capabilities of the robot joints is not a trivial task. This article presents
a novel algorithm—based on the quadratic programming (QP) approach—that allows
for traversing the prescribed task-space path while satisfying joint-space constraints.

2

Algorithm overview

The Predictive Quadratic Programming Inverse Kinematics with Scaling (PQPIK-S)
solves the optimal trajectory planning task by combining the inverse kinematics (IK)
problem with trajectory scaling and solving them simultaneously. The proposed method
is inspired by [1] and emerges from our earlier work [2]. The core of the PQPIK-S is
the quadratic programming (QP) problem:112𝑚𝑖𝑛𝒒̇ ,𝜆 𝛾0 (1 − 𝜆̇) + (𝒒̇ − 𝝋̇)𝑇 𝑾(𝒒̇ − 𝝋̇)2
2
w.r.t. 𝑱𝒒̇ = 𝝂𝜆̇ , 𝒒̇ 𝑚𝑖𝑛 ≤ 𝒒̇ ≤ 𝒒̇ 𝑚𝑎𝑥 , 0 ≤ 𝜆̇ ≤ 1
Joint coordinates are gathered in vector 𝒒. The vector 𝝋̇ defines an additional task
for a redundant robot (such as obstacle avoidance), whereas parameters 𝛾0 and 𝑾 areused to assign weights to different tasks. The end effector velocity v = 𝝂𝜆̇ is parameterized in terms of virtual time 𝜆, allowing to slow down the desired motion if (and onlyif) the joint constraints cannot be satisfied in any other way. Note that the equality constraints rather than the cost functional guarantee that the desired task-space path is traversed. It should also be stated that the equations are discretized at the acceleration level.
Moreover, the QP problem is formulated in such a way that it utilizes the predictionof the manipulator’s future joint states, allowing the scaling to begin sufficiently early.
Outside the prediction horizon, the desired trajectory does not have to be known, allowing for replanning when working in dynamic environments. The obtained joint trajectory is optimal: inside the prediction horizon, it satisfies the end effector trajectory(the main task), fulfills in the best way the secondary tasks (e.g., obstacle avoidance),
and maintains the least possible scaling, all with regard to the joint constraints.

91

The PQPIK-S plays the role of the joint trajectory planner block shown in
Fig. 1 (left). It was implemented in C++ with the use of the Eigen library for linear
algebra and qpOASES containing the active-set solver for the QP problem.

Fig. 1. PQPIK-S flow-chart (left) and overview of control system arrangement (right).

3

Simulations and hardware experiments

Comprehensive simulation studies prove the PQPIK-S’s advantages compared to theclassic IK methods. The most important feature of the PQPIK-S is the ability to satisfy
the joint constraints, slowing down the end effector motion only when needed. Moreover, the PQPIK-S computations are done within a 10-millisecond cycle, allowing for areal-time operation.
The experiments performed on KUKA LWR 4+ redundant robot prove the feasibility of the PQPIK-S-generated joint trajectories. The experiments were performed withthe use of the Fast Research Interface – KUKA’s interface for the communication between the user’s PC and KUKA Robot Controller (KRC)—see Fig 1 (right).

4

Conclusions

A novel method developed in this work proved to be capable of fulfilling the constraints
while traversing the desired path with minimum possible velocity adjustments.
Acknowledgments. This research was partially supported by the National ScienceCentre, Poland grant no. 2022/45/B/ST8/00661.

References
1. Flacco F., De Luca A., Khatib O.: Control of redundant robots under hard joint constraints:
Saturation in the null space, IEEE Trans. Robot. 31(3), 637–654 (2015).
2. Woliński Ł., Wojtyra M.: A Novel QP-Based Kinematic Redundancy Resolution Method
With Joint Constraints Satisfaction, IEEE Access, 41023-41037, vol. 10 (2022).

92Experimental Estimation of Bending of a
Cylinder-Piston Actuator of a Parallel Platform
by Relative Optical Marker Tracking
Christian Brans1 and Andrés Kecskeméthy1
University of Duisburg-Essen, Chair of Mechanics and Robotics, Lotharstr. 1, 47058
Duisburg, Germany[christian.brans, andres.kecskemethy]@uni-due.de,https://uni-due.de/lmr

In the setting of parallel platforms, tracking of bending of actuator legs is
problematic as due to construction restrictions the placement of strain gauges isdifficult and optical markers are impossible to be placed in an absolute coordinate
system whithin the precision needed to track bending (∼ 5µm). In this work,a method is described to track bending out of relative optical measurementswith respect to a bended start position. Fig. 1 shows the parallel architecture
tool machine under investigation, the new R(2RPS-RP)-UPS parallel platform
named ’TriMule’ developed by Prof. Tian Huang in his laboratory in Tianjin [1].
Four optical markers by Leica Absolute Tracker AT901-LR (0.32µm accuracy)
were placed along the horizontal of the RPS limb, which was extended in five
50mm steps y0 ...y5 . The position of the markers were measured relative to aworld reference system aligned with the base coordinate system of the parallel
platform. To avoid errors caused by noise, the experiment was repeated seventimes. For the reproduction of the bending, a Bernoulli beam model of the limb
as an overlap of the cylinder and the piston was implemented in Matlab using
Heaviside functions for the discontinuous changes and an ODE integrator overthe length. In the area of overlap, the bending stiffness and the masses weresuperposed. Moment of inertia of the piston Iy,p and the cylinder Iy,c , Youngmodulus E and density ρ were fitted by numerical optimization such that thebending deflections obtained from the optical tracking for each optical marker
matched in a least square error sense the corresponding displacements of themodel. Joint clearance could be neglected as there was no reverse loading. The
model and the detailed computations are omitted here due to lack of space
0

100

200

300

400

500

600

700

800

900 1000 1100 1200

Position [mm]Base link / Big R-joint

Revolute joint

RP-limb

Spherical joint

Motor

exp.
RP-limb

RPS-limb

Motor

Wrist

E 105 [N/mm3 ]fit.

2.10 2.27

Revolute jointMotorρ 10−6 [kg/mm3 ] 7.75

UPS-limb

Motor

Position

[mm]

Un

z
y

y

7.99

Spherical joint

RPS-limb
rs
ive

a

int
l jo

4

4

Iy,p 10 [mm ]3.92 4.54

54

2.38 2.79

ColumnIy,c 10 [mm ]xFig. 1: Top and side view sketch of parallel platform and fitted parameters

93and will be presented at the conference. The calculated bending lines for everyyi (Fig. 2 b)) are compared with the values of the measurements, showing good
agreement for the first three strokes. For the two larger strokes, the measurement
points seem to deflect less than the model. Also, the fitted moments of inertia are
unrealistically large (Fig. 1, right table). This may be due to the sagging of theend effector at longer strokes by 1µm, which seems plausible. The experimentshows that a relative model-based optical beam deflection sensor may rendersufficient accuracy if effects of sagging of the end-effector are identified andcompensated. Further investigation will foresee an overconstrained guidance ofpistons, sagging, and more involved material and cross-section parameters.
a)

100

0

200

300

E

400

FM otor

A

500

700

600

800

900

1000

1100

z

1200

Position [mm]ByMarker position

Marker position

I

II
Az

ℓI (yi )IIIℓAB (yi )ℓEB (yi )ℓII (yi )BzℓIII (yi )Length of piston
Length of cylinder
Offsetb)c)Fig. 2: a) Beam model of the RPS limb in an arbitrary position, b) calculated
bending lines, c) ∆ bending and measured values

Acknowledgments
This work was supported by EU H2020-MSCA-RISE 2016 (Grant 734272). The
authors wish to particularly thank Prof. Huang Tian and Prof. Liu Haitao from
Tianjin University for their support in their laboratory for the experiment.

References
1. Tian Huang, Chenglin Dong, Haitao Liu, Tao Sun, and Derek G. Chetwynd. A
simple and visually orientated approach for type synthesis of overconstrained 1T2R
parallel mechanisms. Robotica, 37(7):1161–1173, 2019.

94

Efficient walking of the quadruped using passive
linear spring
Pramod Pal1 , Shishir Kolathaya1 and Ashitava Ghosal1
Indian Institute of Science, Bangalore, India1
pramodpal@iisc.ac.in

1

Introduction

Quadruped robots have garnered considerable interest due to their potential invarious applications. The design components of a quadruped, such as link design,
actuation and control systems, compliant foot and sensors, play a crucial role inachieving efficient and stable locomotion. An essential component of attaining
efficient walking in quadrupeds is the design of compliant feet that allow thequadruped to absorb impact forces and store and release energy with each step.
In earlier work, we developed a design of a leg for a quadruped with a linear
passive spring in the foot. Through a combination of rigid body simulations
and experiments, we were able to demonstrate that the range of values of thespring constant at the leg resulted in the highest hopping height, outperforming
legs equipped with spring systems with either higher or lower stiffness[1]. These
results highlight the significance of selecting the optimal linear spring configuration for efficient locomotion in quadrupeds. In this work, we extend the idea ofa linear spring in the legs to all the legs of a quadruped and perform simulationsin MuJoCo – a multi-body simulation platform where contact/impact of the leg
with the ground, the kinematics and dynamics of the legs, torso and other links
of a quadruped can be modeled and taken in to account for simulations[2]. Oneof the key preliminary result is that the designed (and modeled) quadruped can
traverse a longer distance when there is a linear spring in the foot as compared
to a quadruped where the legs are “rigid” with no springs.

2

Simulation results

As mentioned earlier, we have now designed a quadruped with each leg containing a linear spring. The trajectory traced by a foot of the quadruped is shown in
Fig. 2a and it can be seen that the trajectories are similar (bit not exactly thesame) with and without a spring in the leg. The quadruped is made to undergo atrotting gait – front and hind legs on opposite sides move together. Simulations
are done for about 10000 time-steps and the forward motion of the quadruped isshown in Fig. 2b. It can be clearly seen that quadruped traverses (on flat ground)more distance when there is spring in the leg – about 3.5 m versus about 2 mwhen there is no spring.

95

!"#$%

Fig. 1. Snapshot of motion of quadruped 

 




"




)*'+,


 

 


(

!

%

!

+,

"
#
&'

$

%

+-,

Fig. 2. (a)Trajectory of the foot (b)Distance traveled by quadruped

3

Conclusion

This work deals with the simulation of a quadruped with and without a spring(compliance)in the leg. Preliminary results show that the quadruped with compliance cantravel a longer distance as compared to a quadruped with a rigid foot. The work
is continuing and will be validated with hardware results in the future.

References
1. Pramod Pal, Anubhab Dasgupta, Avinash Bhashkar, Shishir Kolathaya, andAshitava Ghosal,Efficient Robot Hopping Mechanisms with Compliance using Evolutionary Methods.In: Proc of 32nd International Conference on Robotics in AlpeAdria-Danube Region, Springer Nature, Bled, Slovenia (2023, Accepted)
2. Todorov E, Erez T, Tassa Y. Mujoco: A physics engine for model-based control.
In2012 IEEE/RSJ international conference on intelligent robots and systems 2012
Oct 7 (pp. 5026-5033). IEEE.

96Kinematics of a Tripod Parallel Continuum
Robot
O. Altuzarra1 , V. Petuya1 , M. Acevedo2 , M. Vizcaı́no2 , and S. Rodrı́guez2
1

University of the Basque Country UPV/EHU, Torres Quevedo s/n, Bilbao 48012,
Spain,
victor.petuya@ehu.es
2
Universidad Panamericana. Facultad de Ingenierı́a. Álvaro del Portillo 49,
Zapopan, Jalisco, 45010, México

A Tripod 3P RS is a lower mobility parallel manipulator with 3 degrees of
freedom whose usual geometrical constraints enforce a 2 rotational and 1 translational type of motion. Nevertheless, some parasitic motions occur on the constrained degrees of freedom accounted for by a set of algebraic constraint equations. Parallel Continuum Manipulators are devices where some elements are
replaced by slender rods whose deformation is the source of mobility, allowing
the elimination of some of kinematic joints. This type of closed-loop compliant
mechanisms have some features that can be useful in certain applications, i.e. thedeformed state introduces a preload that avoids backslash, and their inherent
compliance can be useful in delicate tasks. In this contribution, the kinematic
analysis of a tripod-type parallel continuum manipulator, 3P F S shown in Fig. 1,
is performed; then Workspace and singularity locus are obtained, and positioning
accuracy is evaluated experimentally.

Fig. 1. Flexible Tripod 3P F S with Cosserat Rods

The 3P F S Tripod is a coupled mechanism of flexible rods, where a rigid
end-effector is connected to 3 rods Ai Bi , in which the proximal ends of each rod
are clamped to a vertical linear actuator such that ai = pi (0) = [axi ayi ρi ].
At each configuration, under given load, rods will be deformed pi (s) so that thesystem is in a stable equilibrium pose.

97

The FK consists of determining the pose of the end-effector, i.e pP and thequaternion ẽ, when input values for each rod ρi and a load are imposed [1].
Guess values are required to start a boundary value problem on a vector of
25 geometric and static equilibrium residuals. A Newton method is used in theshooting method and requires the evaluation of a Jacobian of the residue vector
function with respect to the variables of the problem. After each iteration, guess
values are updated and the process starts again until residuals are below a given
tolerance. In Lower Mobility Parallel Mechanisms, dependent output variables
are defined with a constraint analysis. However, this is no longer possible inflexible systems as such hard geometric constraints cannot be imposed. Output
components are obtained with no distinction on whether they are principal (controlled) or parasitic. However, for the IK it is essential to asses appropriately
which components are principal and parasitic. We will show that some translational and rotational ellipsoids can be found to do this. Then, only some output
components are imposed in the IK while the parasitic ones are unknowns of the
problem. Once these Kinematic problems are solved, a workspace analysis canbe performed.
For the prototypes, an actuators’ platform was designed with 3 linear guides
controlled by stepper motors. The electronic control includes a GUI with a MATLAB application that communicates through a serial port with a microcontroller,
allowing the control of the manipulator using direct and inverse kinematic solutions.
For measuring the output coordinates of a manipulator, 6D pose estimation
is used [2]. This computer vision technology provides high-precision estimatesof position and orientation by solving a PnP problem, where the ArUco markers are matched with their 2D projections in the image. Another approach forvalidating the accuracy of artificial vision measurements is through the use ofan accelerometer. In this study, the MMA8451Q three-axis accelerometer sensor
with a 14-bit resolution will be employed. This analysis aids in the determinationof an object’s orientation using a straightforward trigonometry algorithm.

Acknowledgments
The authors thank the financial support received from the Spanish Government(Project PID2020-116176GB-I00) financed by MCIN/AEI/10.13039/501100011033
and the support through Project IT1480-22 provided the Regional Basque Government.

References
1. Black, C.B.; Till, J. and Rucker, D.C.: Parallel Continuum Robots: Modeling, Analysis, and Actuation-Based Force Sensing. IEEE Transactions on Robotics. 34, 29-47(2018) 10.1109/TRO.2017.2753829
2. Wu, G. and Shi, G.: Experimental statics calibration of a multi-constraint parallel
continuum robot. Mechanism and Machine Theory. 136, 72-85 (2019) https://doi.
org/10.1016/j.mechmachtheory.2019.02.013

98

A Novel Integrated Driving and Steering Module and Its
Multi-objective Optimization
Xinbo Chen1, Jiawei Chen1 and Wei Wang2
1 Tongji University, Shanghai 201804, China
2 Tokyo University of Agriculture and Technology, Tokyo 184-8588, Japan

1

Introduction

The integrated driving and steering module allows the vehicle to independently control
the steering angle and driving torque of each wheel. This enables the vehicle to realize
various driving modes such as oblique driving and lateral driving, which improve thevehicle's maneuverability and operating stability. However, the suspension system ofexisting integrated driving and steering modules is typically a sliding pillar type suspension, which makes balancing the mass and structural stiffness of suspension systema challenge. For the modules based on wishbone arm type suspension and trailing arm
type suspension, due to the installation of additional steering motor in the suspension,
the unsprung mass will also increase, affecting the contact characteristics of the wheels.
In order to solve the problem of large unsprung mass in the integrated driving and steering module, this paper proposes a new type of integrated driving and steering module
based on a lasso mechanism, and multi-objective optimization is conducted.

2Structure Introduction

The new integrated driving and steering module proposed is shown in Fig. 1.

a)b)

Fig. 1. The noval integrated driving and steering module. a) Schematic diagram of suspension
structure. b) Schematic diagram of transmission mechanism.

This module adopts a double trailing arm type suspension. The steering motor is installed on the frame, which is different from the existing modules. The steering motor
becomes a part of the sprung mass. Due to the variation of the center distance between
the output shaft of the steering motor and the input shaft of the steering mechanism with99

the height of the wheel jump, this module transmits steering force through a flexible
compound lasso mechanism. The steering mechanism contains a worm gearing, whose
self-locking characteristics help lock the steering angle. This module has the advantagesof 0 kingpin offset, good structural stiffness (especially the longitudinal stiffness), andlow unsprung mass.

3

Multi-objective Optimization

The optimization design of suspension system typically includes optimization of wheelalignment parameters, lightweight design of suspension components, and optimizationof the K&C characteristics. As there is a coupling relationship between the kinematics,
statics and dynamics of the suspension, the traditional serial optimization method requires multiple rounds of iterative calculation. In order to improve the optimization
efficiency, this paper established a multi-objective collaborative optimization model ofthe suspension. The optimization problem is solved by using Isight software and thesequential quadratic programming algorithm.
The established collaborative optimization model is shown as follows:{

min 𝐹(𝑋𝑔 ) = 𝜆1 𝐾 + 𝜆2 𝑆 + 𝜆3 𝐷𝑠. 𝑡. ∑(𝑋𝑔 − 𝑋𝑔∗ )2 ≤ 𝜀(1)In the equation, K is the optimization model for wheel alignment parameters, and eachwheel alignment parameter is derived from the pose change formula based on the RRSS
mechanism; S is the lightweight design model for the trailing arms, and the maximum
stress value of the arms is calculated by the trained radial basis neural network model;
D is the optimization model for vehicle body vibration, and the root mean square valueof the vertical acceleration of the vehicle body is also calculated by the trained radialbasis function neural network model.
Compared to the serial optimization results, the wheel alignment parameters after multiobjective optimization have been optimized with ranges of 45.02% to 87.28%. Only
the longitudinal slip of the wheel center has increased by 17.99%. The mass of the upper
trailing arm has decreased by 8.81%. The mass of the lower trailing arm has decreasedby 8.18%. The root mean square value of the vertical acceleration of the vehicle bodyhas decreased by 11.43%.

4

Conclusion

Through configuration innovation design and multi-objective optimization, the novel
integrated driving and steering module proposed in this paper has a small unsprungmass. The multi-objective optimization method adopted helps to improve the effectiveness and efficiency of suspension optimization. This paper can provide reference forthe design and optimization of integrated driving and steering modules in the future.

100

Investigation of Tribological Properties of Carbon
Coatings Deposited on Polymer Substrate
Youn-Hoo Hwang, YouJin Min and Dae-Eun Kim
Yonsei University, Seoul, South Korea
kimde@yonsei.ac.kr
Keywords: Polymer, friction, wear, DLC (Diamond-like Carbon) coating

1

Introduction

Polymer materials have outstanding properties such as light weight, self-lubricating
ability, chemical stability, and moderate wear resistance. Due to these attractive properties, polymers are used in a variety of mechanical parts such as gear, bearing andseal. However, polymers have relatively low strength and poor wear resistance, which
can lead to early failure of machine parts [1]. In order to minimize these problems andimprove the durability of the polymer, research on fabricating composite materials
with various nanomaterials and polymers is being actively conducted. In this regard,
methods to improve the tribological properties of polymers by depositing protective
coatings need to be further explored.
Diamond-like carbon (DLC) has emerged as a useful coating material due to its
unique combination of mechanical, chemical and thermal properties [2]. DLC has a
low coefficient of friction and high wear resistance, so it can be used to improve thedurability of precision parts. In this study, in order to reduce the wear, DLC coating
was applied to the surface of the polymer, and the frictional properties of the polymer
were investigated in various environments.

2

Method

2.1 Tribological test and analysis
A polytetrafluoroethylene (PTFE) that is widely used in the industry was selected forthe experiments. The DLC coating was deposited on PTFE using a sputtering technique. The experiments were performed using a reciprocating type of tribometer inenvironment chamber. The experiment was conducted three times per specimen ateach condition to ensure reliability. After the test, the wear tracks were measured
using a laser confocal microscope and scanning electron microscope (SEM). The
chemical compositions of the wear tracks were measured by energy dispersive X-ray
spectroscopy (EDS) and Raman spectroscopy.

101

Fig. 1. Schematic of reciprocating type tribometer in the environment chamber

3

Results and conclusions

Comparing the average coefficient of friction between the DLC coated PTFE and thepure PTFE, the DLC coated PTFE had a relatively high friction coefficient. As for thewear behavior, it was found that in general the wear rate was higher in the case of thepure PTFE compared to DLC coated PTFE.
The tribological properties of PTFE and DLC coated PTFE were examined in vacuum environment as well. It was found that one of the important factors causing thedifference in the wear rate of the specimens in a vacuum environment was that thesurface coating inhibited the adhesive wear of pure PTFE during sliding motion.
These results show that DLC coatings can be effectively used to improve the tribological properties of polymers used in various environments.

4 Acknowledgement
This research was financially supported by the Ministry of Trade, Industry and Energy (MOTIE) and Korea Institute for Advancement of Technology (KIAT) through theInternational Cooperative R&D program (Project ID: P0019808)

References
1. Lin, L. Y., Kim, D. -E.: Tribological properties of polymer/silica composite coatings for
microsystems applications. Tribology International. 44(12), 1926-1931 (2011).
2. Liu, Y., Zhang, K., Han, J. -H., Hwang, Y. -H., Xu, S., Kim, D. -E.: One-step method toenhance biotribological properties and biocompatibility of DLC coating by ion beam irradiation. Friction. 10(7), 1114-11126 (2022).

102

Profile optimization in roller bearings for pressure
uniformity
Macareno, L.1[0000-0003-2225-9032] Aguirrebeitia, J.1[0000-0002-0709-9432]
Heras, I.1[0000-0002-1320-7823] Eizmendi, M.1[0009-0006-8415-9634]
1 Department of Mechanical Engineering, Faculty of Engineering in Bilbao.

University of the Basque Country, UPV/EHU, 48013, Bilbao, Spain

1

Introduction

The study of the contact between elastic solids is of great importance in several fieldsof mechanical engineering [1], mainly in tribology. When all the assumptions of Hertz
theory are fulfilled, the relationship among load, deformation, contact area and pressure
distribution are well known. However, for many cases in the practical engineering application, these relationships cannot be obtained in an easy way, and the use of numerical methods such as the Finite Element Method or Boundary Element Method [2] isnecessary. The latter is the one used in this work. By means of this method, a profile
optimization methodology is developed, aiming pressure uniformity in the roller-raceway contact for roller bearings.

2

Development of the method

The BEM was programmed ad-hoc to reach the deformation, contact area and pressure
distribution between an arbitrarily defined roller shape and a cylindrical or conical raceway. Then, the optimization procedure was designed to reach uniform pressure distributions. Bearing design is established upon several variables that are determined by the
specific application in which they are to be used. From the point of view of the designof the rolling elements, the operational variable is the maximum contact force, while
the geometrical variables are the length, the diameter, and the taper angle. Once theraceway is defined, the only geometrical variable that remains the manufacturer's
choice is the type of profile to be applied to the roller. In fact, the choice of the profileis the differentiating characteristic between rollers, and a correct choice is of paramountimportance if the service life of the bearing is to be maximized. This profile is usually
defined by logarithmic functions [3], since they provide a smooth variation of the profile curvature. There are several studies [4] showing methods to optimize these profiles
based on various parameters. All these optimizations are limited by the mathematical
stiffness of the logarithmic function. This work reaches a solution established upon
obtaining the optimum profile using a multipoint method, leaving each point free tomove to create the profile with which the distribution of contact pressures is optimal.
To achieve this solution, the first step is to define an objective function, which consistsof the optimal contact pressure distribution in the mid-contact plane, avoiding pressure103

peaks due to abrupt curvature changes. Considering this, the optimum distribution will
be rectangular, with a constant pressure that will cancel out in the extreme areas of theroller. The method starts from an initial profile and, in each iteration, the difference ofpressures at each point between the obtained distribution and the optimum one is quantified. With these values, a geometric proportional correction is made at each point of
the profile. This operation is repeated iteratively until the chosen norm of the pressure
difference vector is less than a certain value. The method is highly convergent, and its
stability depends on the step size of the proportional adjustment at each iteration. The
number of profile definition points also influences the choice of the step size, as wellas the execution time.

Pressure

Profile

mm

Data
F
Ø
L
Lef

100 KN
45 mm
60 mm
58 mm

Fig. 1. Contact pressure distribution for initial and optimum profiles.

3

Conclusions

This paper presents an iterative numerical method to obtain the optimum profile of therollers in a bearing without using any defined mathematical function.

References
1. Johnson, K. L.: Contact Mechanics, Cambridge University Press, Cambridge, UK (1985).
2. Hartnett M. J.: The Analysis of Contact Stresses in Rolling Element Bearings. Journal of
Lubrication Technology (101), 105-109 (1979).
3. Lundberg, G.: Elastic Contact Between Two Semiinfinite Bodies. Forschung auf den Gebiete des Ingenieurwesen 10(5), 201-211 (1939).
4. Abhijeet V. Salunkhe et al: A Review on Design Optimization of Rolling Contact Bearings.
In: International Journal of Current Engineering and Technology, 7(3) 983-986, Inpressco,(2017)

104

The effect of graphite domain direction on the friction
coefficient of diamond-like carbon measured by polarized
Raman analysis
Takayuki Tokoroyama 1 , Chiro Fujiwara 1 and Noritsugu Umehara 1
1

Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8603, Japan
takayuki.tokoroyama@mae.nagoya-u.ac.jp

Abstract. We focus on the existence of friction induced graphite domains on the
topmost surface of carbonaceous coating. The direction of the incident electricfield can be controlled by rotating the polarizer, and clarify the relationship between the direction of friction and the direction of the graphite domain. Two typesof thin coatings were prepared. One was tetrahedral amorphous carbon nitride(ta-CNx) coating which slid against a Si3N 4 ball in vacuum (=0.013), and theother was in air under room temperature (=0.4). The D peak intensity of low
friction surface induced by parallel incident light showed approximately 20 %increase from 0° to 90°. The high friction surface showed approximately 16.8 %increase from 0 to 40°. The result indicated that friction induced graphite domains
were possibly existed on the topmost surface. Since the low friction coefficientis considered to occur by incommensurate configuration, so it is assumed that thetransfer layer built on counter material will show different direction of the graphite domain due to frictional force.
Keywords: Carbonaceous coating, Graphitization, Polarized Raman.

1

Introduction

The low friction phenomena of carbonaceous coatings are reported its graphitization at
the topmost surface by cyclic friction under nitrogen gas [1]. The low friction mechanism of those coatings due to graphitization is divided that low shearing strength graphite sheets were generated at the topmost surface, or graphite domains generated on the
topmost surface arranged incommensurate position [2] between transfer layer and its
coating. A measurement method capable of detecting the direction of graphite domains
formed by friction is interesting. Raman spectroscopy can detect the collective behaviorof carbon atom clusters constituting graphite domains [3]. Furthermore, it is assumed
that polarized Raman spectroscopy [4], which can control the direction of the incident
electric field, can be used to evaluate the direction of graphite domains formed due tofriction. In this study, we focus on the existence of such friction induced graphite domains so that we built the direction of the incident electric field can be controlled byrotating the polarizer, and clarify the relationship between the direction of friction andthe direction of the graphite domain.

105

2

Experimental method

A half-wave plate was set among the light source and an optical microscope lends canrotate the polarization of the incident laser beam. The polarizer can rotate 2° of accuracy. The measurement by using the polarizer is divided two types; the incident ligh tpolarizer and scattered one is same direction as parallel, and the incident and scatteredis perpendicula r. Two types of thin coatings were prepared. One was tetrahedral amorphous carbon nitride (ta -CNx) coating which slid against a Si3 N4 ball in vacuum(5.0×10 -4 Pa). The other was slid in air under room temperature. The surface preparedin vacuum showed approximately 0.013 of friction coefficient, and the surface of in air
showed approximately 0.4. The normal load was 0.19 N, sliding speed was 15.7 mm/s
under room temperature.

3

Results and discussion

The polarized Raman analysis for low friction coefficient surface (in vacuum) with 10 °from 0° as parallel to the friction direction to 90° was conducted as shown in Fig. 1(a)of D peak intensity, and high friction coefficient surface in air; Fig. 1(b). The D peakintensity induced by parallel incident light showed approximately 20 % increase from0° to 90°. On the other hand, the high friction surface showed approximately 1 6.8 %increase from 0 to 40°. The D intensity is related to the graphite edge direction [4],therefore, the result indicated that friction induced graphite domains were possibly existed on the topmost surface as illustrated in Fig. 1(c) and (d). Since the low friction
coefficient is considered to occur by incommensurate configuration, so it is assumed
that the transfer layer built on counter material will show different direction of thegraphite domain due to frictional force.
3000

ta-CNx disk (vs. Si3N4 ball in vacuum)
Laser wavelength: 532 nm

2500

(a)
D peak intensity

D peak intensity

3000

2000

20.2 % up⇑

1500
1000

Parallel
500

ta-CNx disk (vs. Si3N4 ball in atmosphere)
Laser wavelength: 532 nm

2500

Armchairarrangement

16.8 % up⇑

1500

9.1 % up⇑Armchairarrangement

90 o Sliding

1000

direction

Armchair

30

60

90

Measurement angle of incident light q, o

40 o Sliding

direction(d)Parallelarrangement
Perpendicular

500
0

0

Sliding
40 o direction

2000

Perpendicular0

Sliding
90 o direction
(c)

(b)

0

30

60

90

Measurement angle of incident light q, oArmchairarrangement

Fig. 1. The D peak intensity as a function of incident light direction (a) low friction in vacuumand (b) high friction in air (c) The D peak intensity as a function of incident light direction of
low friction in vacuum and (d) high friction in air.

References
1. H. Inoue, S. Muto, X. Deng, S. Arai and N. Umehara: Thin Solid Films. 616, 134 (2016).
2. M. Dienwiebel et. al.: Phys. Rev. Lett. 92, 126101 (2004).
3. A.C. Ferrari and J. Robertson: Phys. Rev. B. 61, 14095 (2000).
4. C. Casiraghi et. al.: Nano Lett. 9, 4, 1433 (2009).

106

The tribological properties of DLC coating with B/Cr codopants and clarification of the mechanism at 300oC
Ruixi Zhang1, Woo-Young Lee1,2, Noritsugu Umehara1, Takayuki Tokoroyama1,
Motoyuki Murashima1,3, Yuji Takimoto4
1 Department of Micro-nano Mechanical Science and Engineering, Nagoya University, Japan
2 Intelligent Optical Module Research Center, Korea Photonics Technology Institute, Korea
3 Department of Mechanical Systems Engineering, Tohoku University, Japan
4

Toyo Tanso Co.,Ltd., Japan
Corresponding author’s E-mail address: ruixi.zhang@mae.nagoya-u.ac.jp

1

Preparation of a-C:B:Cr coating and its mechanicalproperties

Diamond-like carbon (DLC) coatings, which have widespread applications in many
fields due to their low friction, high wear resistance, and other excellent tribologicalbehaviors, have been regarded as a promising candidate of solid lubricants for many
years [1]. However, it was found that hard DLC coating became dramatically wornout since 200oC, thus researchers have been trying to explore new DLC coatings to
improve their thermal resistance and tribological properties at high temperature. The
current common method is to dope additive elements such as boron, silicon, or certaintransition metals into DLC coatings [2]. In recently years, the rapid development of
FCVA made it possible to deposit doped-DLC coatings by adding dopant elements
into graphite target. However, the optimal deposition of doped-DLC coating and its
high-temperature tribological properties have not been clearly studied yet.
In this research, boron and chromium (B/Cr) co-doped DLC coating were preparedby T-shaped FCVA deposition facility. Argon gas with different flow rate was introduced to maintain the deposition continuity, compensating the extinguishment of arc
discharge caused by additive elements. Three different graphite targets with various
chromium contents (0.5, 1 and 3, at. %) were adopted to deposit different a-C:B:Cr
coatings with more than 100 nm thickness. The mechanical properties were evaluatedby the nano-indenter (ELIONIX INC.: ENT-1100a), demonstrating that a-C:B:Cr
coatings with 10 GPa hardness can be prepared, shown in Fig.1. Besides, the analysis
by Raman spectroscopy (JASCO Corporation: NRS-1000) revealed that the additive
Cr element improved ID/IG ratio of pristine a-C:B:Cr coatings, thus the more “graphite-like a-C:B:Cr coatings” exhibit softer hardness than a-C:B coating,as well as a-C
coating.

Fig.1. Mechanical properties of
a-C:B:Cr coatings with various
Cr concentrations

Fig.2. Tribological properties of aC:B:Cr coatings with various Cr concentrations at 300oC
107

2

Tribological properties of a-C:B:Cr coating and its
mechanism at 300oC

Three different Cr-containing a-C:B coatings (0, 1, 3 at.%) were used to estimate thetribological properties. Friction experiments were conducted by a pin-on-disk tribometer tester in ambient air with the temperature of 300oC. Si3N4 balls were employed
to press against the rotating a-C:B:Cr disk (Φ8mm) with a normal load of 1.0 N. Besides, the experiments were carried out at a rotating speed of 200 rpm and sliding
radius was 3 mm. Results of tribological properties of each a-C:B:Cr coating wereshown in Fig.2, illustrating that a-C:B:Cr1 coating exhibited ultra-low friction with theaverage friction coefficient of 0.02, as well as high wear resistance with specific wear
rate less than 5×10-6 mm3/Nm. The results also demonstrated that a-C:B:Cr1 coating
was the optimal one among the three various Cr-containing a-C:B coating, Raman
analysis on the tribo-film adhered on the Si3N4 balls, as shown in Fig.3, proved thatgraphite-like transfer film was formed on the Si3N4 counterpart, where the softest aC:B:Cr1 coating might be easiest to realize graphitization and cause low friction.
Meantime, the rich C-B bonds in the wear track of a-C:B:Cr coating measured by Xray Photoelectron Spectroscopy (XPS) was considered as the reason of high wear resistance athigh temperature for the a-C:B:Cr1 coating,since B4C nanoparticles were proved to be one
factor to improve the wear resistance under hightemperature.

Conclusion
A DLC coating with co-doped elements is designed for the high temperature, its mechanicaland tribological properties are evaluated. The aC:B:Cr1 coating is found to realize the low friction and high wear resistance. The graphitization and the formation of B4C nanoparticles are
believed to be the reason of low friction andhigh wear resistance, respectively.

Fig. 3. Surface analysis of Raman
spectroscopy on balls and XPS on
disks

References
1. Robertson, J., “Diamond-Like Amorphous Carbon,” Material Science and Engineering R,
37, 2002, 129-281.
2. Camargo Jr, S. S., Baia Neto, A. L., Santos, R. A., Freire Jr. A. L., Carius, R. and Finger,F., “Improved High-Temperature Stability of Si Incorporated a-C:H Films,” Diamond
Relat. Mater., 7, 8, 1998, 1155-1162.

108Effect of Fracture Toughness on Wear of DLC Coatings
Yusei Yamada1 , Motoyuki Murashima2 , Noritsugu Umehara1 ,Takayuki Tokorfoyama1 and Woo-Young Lee 3
1 Nagoya University, Nagoya, 464-8603, Japan
2 Tohoku University, Sendai, 980-8579, Japan
3 Korea Photonics Technology Institute, Gwangju, 61007, South Korea

noritsugu.umehara@mae.nagoya-u.ac.jp

1

Introduction

Diamond-like carbon (DLC) coatings, which are one of amorphous carbon coatings,
have many applications due to low friction, high hardness, high wear resistance. Hardmaterials would have brittleness, so we should avoid the intrinsic fracture of DLC coatings. However it is quite difficult to evaluate the intrinsic fracture properties of DLC
coatings and obtain the effect of the fracture properties on wear properties of DLC
coatings.
In the present study, we demonstrate a comprehensive study showing a detailed relation
between quantitative values of fracture toughness and wear under severe contact conditions. To obtain coatings with various fracture toughness, we prepared a variety of
DLC coatings: ta-C:H, a-C:H, and ta-C coatings with different carbonaceous structuresand surface roughness. As a result, the present paper clearly illustrates that the wear
behavior of DLC coatings can be categorized into two trends; one with fracture and theother without fracture. Finally, we conclude that the wear behavior of the DLC coatingsstrongly depends on the parameter of K/KIC, which is expressed with a fracture toughness and a stress intensity factor.

2

Experimental

Nine types of DLC coatings were deposited on a silicon substrate: two a-C:H coatings,
one ta-C:H coating, and six ta-C coatings. Fracture toughness of these DLC coatings
were measured by indentation method. Nastasi et al. demonstrated an improved method
to evaluate fracture toughness from the crack length formed on DLC coatings/Si-substrate system [1]. The fracture toughness of the system was measured as a combination
between the total fracture work and the composite modulus of the system (including asubstrate and a coating). Therefore, a critical fracture toughness of a coating KIC(Eq.(1)) is given by the following Eq.(2)𝐾IC = √𝐺𝑓 𝐸𝑓

(1)

109

𝑐0 3
2𝑑 𝐺𝑓 𝐸𝑓
( − − 2)[( ) − 1] =𝑐𝜋𝑐 𝐺𝑠 𝐸𝑠

(2)

Where KIC is the fracture toughness of the coating, Gf is the work of fracture in thecoating (fracture energy of the coating), and Ef is the Young’s modulus of a coating. In
the Eq.(2), c0 is the half radial crack length in the uncoated substrate, c is the half radialcrack length in the coating/substrate system at the same indentation load, d is the coating thickness, Gs is the work of fracture in the substrate (fracture energy of the substrate), and Es is the Young’s modulus of the substrate. Friction test were conductedunder dry air condition with a Pin-on-Disk friction tester. Stress intensity factor K was
estimated from stress and estimated initial crack length from surface roughness under
the friction conditions. Figure 1 shows the relation between specific wear rate and
K/KIC. The figure presents a clear trend that the specific wear rate increases with theincrease of the K/KIC.

Specific wear rate w,
x10-7 mm3/Nm

50

DLC coated Si-wafer vs. SUJ-2 ball in PAO4
-Sliding speed V, 0.042 m/s-Load W, 1 N and 10 N
-Temp. t, 80 oC-Duration T, 60 mins.

40
30□ a-C:H

20◇ ta-C:H10〇 ta-C (at 10 N)△ ta-C (at 1 N)

0
0

0.2

0.4

0.6 0.8
K/KIC

1.0

1.2

Fig. 1. Relation between specific wear rate and K/KIC of the DLC coatings.

3

Conclusion

The ratio of stress intensity factor to the critical fracture toughness K/KIC was introduced, and the specific wear was characterized by K/KIC. The relationship between
K/KIC and specific wear rate showed good linear relationship, where the specific wear
rate increased with increasing K/KIC. In the case DLC coatings with K/KIC of more than0.4, the main wear mechanism was fracture. On the other hand, for coatings with K/KIC
of less than 0.1, fracture did not occur under friction.

References
1. Nastasi M, Kodali P, Walter KC, Embury JD, Raj R, Nakamura Y. Fracture toughness of
diamondlike carbon coatings. J Mater Res 1999;14:2173–80

110Development of low-friction DLC surface with liquid film
derived from the air using dielectric barrier discharge
Wenjun Wu 1, Noritsugu Umehara 1, Takayuki Tokoroyama 1, Motoyuki Murashima 2
and Ruixi Zhang 1
1

1

Department of Micro-Nano Mechanical Science and Engineering, Nagoya University, Japan2
Department of Mechanical Systems Engineering, Tohoku University, Japanwuwenjun@ume.mech.nagoya-u.ac.jp

Introduction

Diamond-like carbon (DLC) is a fascinating material as a solid lubricant, and its hybridization of sp2 and sp3 structure provides the anti-friction, and wear-resistancecharacteristics. From these advantages, it is attracting research attention and is widelyin the spotlight throughout mechanical applications. It has been reported that the tribomicroplasma reaction caused the production of polymers on the friction surface that
reduce the friction coefficient [1]. Thus, the friction characteristics of the DLC coating can be controlled by acting on the DLC coating with the simulated tribomicroplasma. In this study, we developed a new surface treatment method by using dielectric barrier discharge (DBD) to achieve low damage treatment, which resulted in low
friction. DBD is a type of non-thermal plasma formed when an AC voltage is applied
across two electrodes separated by a dielectric barrier.

2

Experimental method

The tetrahedral amorphous carbon-containing nitrogen (ta-CNx) coating was deposited on SUJ2 disks by using the ion beam assisted filtered arc deposition (IBA-FAD)
system. A T-shaped filter was used to eliminate macro-droplets to improve the coating quality. The effect of in-situ irradiation of DBD on the friction behavior of ta-CNx
coatings was elucidated by using a ball-on-disk tribometer. In the friction test, a normal load of 0.98 N and a sliding speed of 38 mm/s were used.

3

Results

The friction test results and the effect of DBD irradiation on friction reduction are
shown in Fig. 1. The results show that the average friction coefficient of ta-CNx isapproximately 0.25 before DBD irradiation, and then decreases sharply to 0.01 after
the third DBD irradiation. And a liquid film was observed on the surface. And after
the first and second DBD irradiations, the friction coefficient returned to about 0.25.
The reason may be that the liquid film could not be produced when the DBD irradiation was stopped.

111

Figure 2(a) shows the FTIR result. It shows that the liquid film produced in humid
air contains large amounts of CH, NH, NO, and OH bands. The LC/MS results areshown in Fig. 2(b), and the results indicate that the liquid film contains nitrate ions.
And the liquid film was analyzed using the pH test paper, revealing a pH value of 2
(strong acid).

Fig. 1. The effect of DBD irradiation on friction reduction

Fig. 2. Analysis results of liquid films using FTIR (a) and LC/MS (b).

4Conclusion

In this study, we developed an in-situ surface treatment method for DLC coating using DBD. After DBD irradiation, the friction coefficient decreased from 0.25 to 0.01.
In particular, when the humid air was blown to the DBD irradiation location, it wasobserved that a liquid film was produced on the DLC coating. Therefore, it can beconsidered that the CH, OH, NO, and NH bands in the liquid film are important for
reducing friction. And in-situ production of acidic lubricants using DBD can be used
to achieve low friction.

References
1. Nakayama K, Hashimoto H.: Triboemission, tribochemical reaction, and friction and wear
in ceramics under various n-butane gas pressures. Tribology International.29(5), 385–393,(1996).

112

Tribo-corrosion properties of hard carbonaceous coatings
Lulu Li1, Noritsugu Umehara 1, Takayuki Tokoroyama 1, and Ruixi Zhang 1
1 Department of Micro-Nano Mechanical Science and Engineering, Nagoya University, Japanlilulu@ume.mech.nagoya-u.ac.jp

1

Introduction

From the viewpoint of combustion engines used in marine environments, the wet andsalt-rich environments, particularly NaCl and water vapor, make the hot components(such as compressor blades) suffer mechanical wear, variable temperature, and corrosion simultaneously during operation. High hardness, high corrosion proof, and low
friction material are desired. One of the candidate materials is hard carbonaceous coating such as tetrahedral amorphous carbon (ta-C) which has high hardness and chemical
inertness. The tantalum element has also been proven to exhibit good high-temperature
resistance and corrosion resistance. However, it is unclear whether the material can
perform low friction (no more than 0.05) under corrosive situations.
This study conducted a friction test for ta-C, tantalum doped ta-C: Ta, and double
layers ta-C/ta-C: Ta coatings to understand basic corrosion-proof ability under NaClsolution. The effect of microstructure changes and ions of NaCl solution on the friction
process is also clarified.

2

Experiment method

For depositions of ta-C, ta-C: Ta, and ta-C/ta-C: Ta coatings, a hybrid coating system
was used, which includes an anode-layer closed-drift linear ion source (LIS), unbalanced magnetron sputter (UBMS), and filtered cathodic vacuum arc (FCVA).
For the friction process, a ball (Si3N4)-on-disk (coating) type was used under 3.5 wt%
NaCl solution (according to references) with temperatures of 15°C and 80°C. After thefriction test, the optical microscope observed the wear track of the disk and ball. Raman
spectroscope (RENISHAW in Via Reflex, England) was employed to identify
the chemical structure with a 532-nm laser and 1800 lines/mm grating.

3

Experiment result

The optical microscope and Raman spectra of disk and ball wear areas (80°C) are
shown in Fig.1. For the ta-C and ta-C: Ta coating, the obvious wear debris can be observed on the disk. From the Raman result, the wear area of the ta-C coating shows a
W-O peak around 690 cm-1 from the substrate, which indicates the damage to the coating during the friction process. With the Ta doped, the wear area on the ta-C: Ta coatingshows obvious peeling off, which may be the reason for the fluctuating friction
1113coefficient (up to 0.15). For the ta-C/ta-C: Ta coating, the obvious Ta-O peak around670 cm-1 was observed on the wear area without any W element and peeling off. The
wear area on the counterpart ball of ta-C/ta-C: Ta coating also shows a more continuousand dense friction film than ta-C and ta-C: Ta coating. From the Raman result, the Dpeak and G peak show a higher intensity for the friction film on the counterpart ball of
ta-C/ta-C: Ta coating.
To compare the effect of corrosive NaCl solution on the friction properties, the wear
area Raman result of disk and ball on the pure water was also conducted. Ta-O peak on
the disk wear area was not sharp and the intensity was as same the as-deposited coating.
Besides, the intensity of the D peak and G peak was lower than that in NaCl solution.
Therefore the NaCl solution has a positive effect on the formation of Tantalum pentoxide [1,2]. Tantalum oxide is the N-type oxide with a number of oxygen vacancies. Whenthe coating was immersed in the NaCl solution, Ta5+ was replaced by the Na+, which
reduced the electrical conductivity of the oxide and increased the formation of Ta-O[3].

Fig. 1. Optical microscope and Raman images of wear areas, a: ta-C coating; b: ta-C: Ta coating;c: ta-C/ta-C: Ta coating.

4

Conclusions

The ta-C/ta-C: Ta coating can reduce the friction coefficient by the formation of Ta2O5
and carbonaceous friction film. NaCl solution can have a positive effect on the reduction of friction coefficient by the replacement of Na+ to promote the oxide formation.

References[1] Yongsheng Chen, Israel E. Wachs: Tantalum oxide-supported metal oxide (Re2O7, CrO3,
MoO3, WO3, V2O5, and Nb2O5) catalysts: synthesis, Raman characterization and chemicallyprobed by methanol oxidation. Journal of Catalysis 217, 468–477 (2003).
[2] V. N. Kruchinin, V. A. Volodin, T. V. Perevalov: Optical Properties of NonstoichiometricTantalum Oxide TaOx (x < 5/2) According to Spectral-Ellipsometry and Raman-Scattering Data.
Optics and Spectroscopy 124, 808–813 (2018).
[3] B. Prakash Æ J. P. Celis: The Lubricity of Oxides Revised Based on a Polarisability Approach. Tribology Letters 27, 105–112 (2007).

2

114

Contact behavior of a sliding spherical indenter at
supersonic speed
Se Jun Shim, Hyeonggeun Jo, Ilkwang Jang and Yong Hoon Jang*
School of Mechanical Engineering, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul
120-749, Republic of Korea* jyh@yonsei.ac.kr

Sliding contacts have become a subject of intense research due to their potential applications across a wide range of speeds, from low-speed brakes to high-speed systems
such as rocket-sleds, rail guns, and interactions with air friction during spaceflight.
Numerous studies have investigated sliding contact problems in various dimensions
and speed ranges. Cole and Huth [1] examined a two-dimensional space with line
forces, while Georgiadis and Barber [2] identified errors in the proposed displacement
field for transonic speeds. Craggs and Roberts [3] demonstrated the relationship between sliding object velocity and Rayleigh wave speed. Georgiadis and Barber [4] presented contact pressure based on object shape at different speeds, offering acceptable
solutions for various speed regions.
Barber [5] proposed solutions for normal surface displacement in three-dimensionalsliding, specifically for point forces at different speeds. Rahman [6] analysed contactpressure distribution when a rigid sphere slides on an elastic half-space at sub-Rayleighsubsonic speed, revealing an expanding contact area with increasing sliding velocity.
Georgiadis and Lykotrafitis [7] extended their research on displacement caused bypoint forces, incorporating diverse scenarios such as thermal interaction, friction, surface vibration, and finite element analysis.
Understanding non-conforming contact sliding behaviour for 3D object shapes, particularly when sliding speeds exceed dilatational speeds, remains limited. Singular behaviour of contact pressure within specific contact areas and the presence of anticipatedlinear contact pressure pose challenges, influenced by kinematic considerations.
In this study, our objective is to numerically analyse the distribution of contact pressure in a three-dimensional space under steady-state conditions. Specifically, we investigate the scenario where a frictionless, rigid spherical object slides on an elastic halfspace at supersonic speeds. To accomplish this, we employ the integral equation forcontact pressure, incorporating the gap function and contact condition equation basedon Barber's proposed Green function solution [5]. Our primary focus is to present thefindings regarding the contact pressure distribution and contact area within the regime
where the sliding speed exceeds the dilatation speed. This critical range of analysis
holds significant importance for understanding the behaviour of the system.
Examining the typical distribution of contact pressure, as depicted in Figure 1, we
observe that it corresponds to the contact pressure distribution when the sliding speedis 2.5 times the shear speed (represented by 𝑐𝑐2 ). The contact region can be categorized
into two distinct areas based on the magnitude of the sliding speed. The first area resides

115

near the contact edge, where the propagation of the dilatation wave occurs. The second
area lies beyond, where the Rayleigh wave propagates.
Notably, within the region characterized by dilatation speed and wave propagation,
the contact pressure exhibits a linear pattern, aligning with the predictions from thetwo-dimensional results. Additionally, the contact surface assumes a spherical or ellipsoidal shape. These outcomes emphasize the influential role of kinematics in the contact
analysis, thereby shaping the observed results.
By conducting this comprehensive investigation, we contribute to the understandingof contact pressure distribution and its dependence on various factors within the given
sliding scenario.

Fig. 1. Contact pressure distribution in supersonic sliding speed of 𝑉𝑉 = 2.5𝑐𝑐2 .

Acknowledgment: This work was supported by the National Research Foundation of
Korea(NRF) grant funded by the Korea government(MSIT) (No.2021R1A2C3010731).

References
1. Cole, J.D., Huth J.H.: Stresses produced in a half plane by moving loads. ASME J. Appl.
Mech. 25, 433-436 (1958).
2. Georgiadis H.G., Barber J.R.: Steady-state transonic motion of a line load over an elastic
half-space: The corrected Cole/Huth solution. ASME J. Appl. Mech. 60, 772-774 (1993).
3. Craggs J.W., Roberts A.M.: On the motion of a heavy cylinder over the surface of an elastic
solid. ASME J. Appl. Mech. 34, 207-209 (1967).
4. Georgiadis H.G., Barber J.R.: On the super-Rayleigh/subseismic elastodynamic indentation
problem. J. Elast. 31, 141-161 (1993).
5. Barber J.R.: Surface displacements due to a steadily moving point force. ASME J. Appl.
Mech. 63, 245-251 (1996).
6. Rahman M., Barber J.R.: Exact expressions for the roots of the secular equation for Rayleighwaves. ASME J. Appl. Mech. 62,250-252 (1995).
7. Georgiadis H.G, Lykotrafitis G.: A method based on the radon transform for three-dimensional elastodynamic problems of moving loads. J. Elast. 65, 87-129 (2001).

116

Highly Flexible Stretchable Strain Sensor with Sensitivity
and Durability for Human-Motion Detection
Sung-Jun Lee [0009-0001-1059-6050], Dae-Hyeon Kim [0009-0009-3461-301X] and Chang-Lae
Kim*[0000-0002-1983-0181]
Department of Mechanical Engineering, Chosun University, Gwangju 61452, Republic of Korea*kimcl@chosun.ac.kr

1

Introduction

Stretchable and flexible electronics have been widely used in e-skin, wearable electronics, and strain sensors [1]. In particular, flexible strain sensors are attracting great
attention in various fields, such as medical monitoring, human-machine interaction, andelectrocardiogram sensors, due to their excellent efficiency in converting changes inhuman body movement into electrical signals [2]. Generally, strain sensors are composed of conductive materials and flexible elastomers to detect human motion [3]. To
monitor human motion, strain sensors must meet the requirements of elasticity, highsensitivity, fast response and recovery, and durability [3]. Additionally, the durabilityof the strain sensor must be high enough not to be affected by human activity. Althoughconsiderable research has been done on strain sensors over the past few decades, fabricating a sensor with both high durability and sensitivity remains a challenge. Among
various fabrication processes, spray coating was chosen in this work to impart conductivity to the elastomer. Compared to the typical sputtering deposition method, spraycoating enabled thickness control and rapid fabrication.
In this study, we report a strain sensor with improved durability. This strain sensor
was fabricated by embedding CNTs in polydimethylsiloxane (PDMS). By controllingthe curing degree of PDMS, the optimized strain sensor exhibits excellent sensitivity
and durability. Strain sensors made with a simple production process can be applied tosensors for detecting human motion.

2

Experimental Methods

Prior to spray coating, commercially available CNTs were dispersed at a concentrationof 3 wt% in isopropyl alcohol. The CNTs were successfully embedded in the PDMS
surface through the curing parameters of PDMS. A multimeter and a sheet resistancemeter were used to investigate the electrical characteristics of the fabricated strain sensor. Additionally, we investigated the durability of the strain sensor according to thedegree of curing of PDMS through repeated deformation tests and friction tests. The
resistance and friction coefficient were monitored in real-time to obtain signals for repeated deformation and sliding cycles. The shape of the wear track was observed toconfirm the wear resistance according to the degree of CNT embedding.

117

3

Results and Discussion

The electrical properties of CNT-embedded PDMS were considerably varied by controlling the curing degree of PDMS. These electrical changes showed a big differencein the electrical durability of each sensor. Additionally, different types of strain sensors
exhibited significantly different friction/wear characteristics. That is, in the case of asensor with a short pre-curing time of PDMS, it was confirmed that the electrical durability was quite stable. Therefore, it was suggested that the thickness of the CNT coating
layer embedded in the PDMS surface has a significant effect on the electrical and tribological properties. Overall, the experimental results suggest that the degree of curing of
PDMS can play an effective role in improving the performance of strain sensors.

4

Conclusions

Highly flexible and durable strain sensors using PDMS-based composites in which
CNTs are embedded by controlling the curing degree of PDMS have been fabricatedthrough a simple and efficient spray coating process. The experimental results showthat these strain sensors exhibit excellent stability and high durability from 0-100%
strain. Furthermore, the CNT embedded layer according to the curing degree of PDMS
plays a significant role in the electrical properties and wear resistance of the fabricatedstrain sensor. Interestingly, as the pre-curing time of PDMS is shortened, the electricalconductivity and wear resistance show opposite trends, which suggests the potential totune the properties of the sensor. These results indicate that the strain sensor has great
potential in the field of wearable electronics, as it can detect both large and small humanbody movements with high sensitivity and durability.

Acknowledgment
This research was supported by Basic Science Research Program through the National
Research Foundation of Korea (NRF) funded by the Ministry of Education(2021R1I1A3059770).

References
1. Kim, S. O., Han, C. J., Kim, Y., Kim, K. S., Kim, D. U., Lee, C. R., Kim, J. W.: Fabricationof a bending-insensitive in-plane strain sensor from a reversible cross-linker-functionalized
silicone polymer. ACS Applied Materials & Interfaces 12, 6516-6524 (2020).
2. Fan, K., Wei, W., Zhang, Z., Liu, B., Feng, W., Ma, Y., Zhang, X.: Highly stretchable, selfhealing, and adhesive polymeric eutectogel enabled by hydrogen-bond networks for wearable strain sensor. Chemical Engineering Journal 449, 137878 (2022).
3. Lee, S. J., Kim, C. L.: Highly flexible, stretchable, durable conductive electrode for humanbody-attachable wearable sensor application. Polymer Testing 122, 108018 (2023).

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