bluuebunny/crossref_metadata_2025 huggingface dataset:
The Generating Space for Parabolic Motion Error Spiral Bevel Gears Cut by the Gleason Method
Authors: Gosselin Claude , Cloutier Louis
Published: March 2021

Because of their inherent pseudo-conjugate natures, spiral bevel gears cut by the Gleason method basically transmit motion in a non uniform manner. This motion non uniformity, or motion error, repeated at each tooth engagement and at high speeds and loads, can cause vibrations in transmissions and contact-entry impact loads on gear teeth which affect the life of a gearset. It is customary to make small changes to machine settings in order to produce gear pairs with vastly improved kinematics. Therefore, machine setting changes must be carefully chosen such as to produce appropriate unloaded kinematical motion error that will cancel tooth bending deflection and contact deformation at a given load, and thus reduce noise and vibrations due to motion non-uniformity.

This paper presents a study on the effects of machine settings, such as cutter tilt, machine center to back and offset, on the unloaded kinematical motion error. Applying CAD Boolean operations on the results, it is found that, for a given speed ratio, an infinite number of cutter tilt, work offset and machine center to back combinations will produce gear sets with convex parabolic motion error curve of any desired amplitude. Moreover, the amplitude of motion error curves can be linked directly to contact bias on the tooth flank. Thus, gear sets with any parabolic motion error in the unloaded state can be produced, such as to cancel tooth bending deflection and contact deformation in the loaded state.
Effect of Lubricant Jet Location on Spiral Bevel Gear Operating Temperatures
Authors: Handschuh Robert F.
Published: March 2021

An experimental study was conducted to determine the effect of lubricant jet location on spiral bevel gear bulk temperatures. Transient surface temperatures were also measured. Tests were conducted on aircraft quality spiral bevel gears in a closed-loop test facility. Thermocoupled pinions and an infrared microscope were used to collect the pertinent data. A single fan jet lubricated the test gears. Lubricant flow rate (lubricant jet pressure) and applied torque were also varied. The results of this study showed that jet placement had a significant effect on the gear bulk temperatures.
Load Distribution Analysis of Journal Bearings Operating Under Mixed Lubrication Conditions
Authors: Ramamohana Rao A. , Mohanram P. V.
Published: March 2021

When the lubricant film that separates two loaded members becomes thin enough, the asperities on the surfaces begin to interfere. Hydrodynamic journal bearings invariably experience this phenomenon during starting and stopping which is called mixed lubrication. In this case, a part of the applied load is carried by the hydrodynamic action of the fluid film and the remainder through asperity contacts. The part of the load supported by the asperities is significant in that it determines the wear life of the bearing to a large extent. In this work, analytical procedures for the determination of these two components of load based on statistical nature of surface topography have been developed. An algorithm for the estimation of limiting load from wear consideration has been presented. The effect of variation of typical surface topography parameters which undergo change during wear process viz. standard deviation of profile sum, combined radius of curvature of asperities, on hydro-dynamic and asperity load supporting capabilities and true area of contact has been discussed. The computations have been illustrated with experimental data.
Belt Slip: A Unified Approach
Authors: Gerbert Göran
Published: March 2021

Slip measurements on thick flat belts, V-belts and V-ribbed belts running on small pulleys reveal that the slip is much higher than can be predicted with classical creep theory. Shear creep plays an important role and special care must be taken when analysing the shear deflection of the V-belt and the ribs of the V-ribbed belt. Other mechanisms are present as well. The behaviour in the seating and unseating regions changes the direction of the frictional forces in these regions on the driver pulley.

A unified slip theory is presented for flat belts, V-belts and V-ribbed belts considering creep, shear, seating/ unseating and compliance. Measurements and theory fit very well for practical tension levels. At low tension the measured slip is higher than the predicted one for V-belts and V-ribbed belts, which probably depends on the poor fit between the belt and the grooved pulley.
A Closeness Degree Method for Multi-Objective Optimization of Belt Transmission
Authors: Qun Lin , Meijuan Wu
Published: March 2021

A mathematical model for multi objective optimization design of belt transmission is proposed in this paper. The normal fuzzy distribution is used to convert the ideal and non-inferior solutions into fuzzy subsets over the space of objective function values. The optimal solution which is closest to the ideal one could then be found on the basis of closeness degree method.
Limiting Conditions in Gear Shaping With Allowance for Trimming
Authors: Sankaranarayanasamy K. , Shunmugam M. S.
Published: March 2021

Gear shaping process is a generation process by which precision gears can be produced. In some cases, because of the generation motions, interference conditions exist in the process. These interferences may introduce preferable conditions on the gears produced, in a few cases. Such limiting conditions are presented here, after allowing for the trimming of the profile due to these interferences.
Eigensolutions of Damped Torsional Systems
Authors: Huang Yuan Mao , Kon L. G.
Published: March 2021

This study eliminates the conventional assumptions that the disks are rigid with infinite stiffnesses and shafts are very slim with negligible stiffnesses for the equivalent mass-elastic system. Both ends of the damped system can be free or fixed.

The extended transfer matrix method is used with Newton. Raphson technique. A mathematical model is derived and a computer code is generated to determine the eigensolutions of the system. The calculated results are compared and show good agreement with the available data. Therefore, the tool can be used to predict the performance and to design power trains.
Driven Pulley Jumping of Timing Belts
Authors: Gerbert Göran
Published: March 2021

A model and criterium for the jumping limit torque of timing belt drives are presented. The following parameters are considered: pulley geometry, belt geometry, belt strain stiffness, belt tooth stiffness, belt flexural rigidity, shaft stiffness and initial tension. Friction is important in separating jumping on driver and driven pulleys since the jumping behaviour is different at the two sides. Other parameters might influence the jumping limit torque as well. Moreover, great care must be taken to get good parameter data from the test setup.

The present analysis is restricted to driven pulleys. Calculated results of jumping limit torque and shaft load are presented for an XL-belt drive. The results exhibit the same behaviour as test results presented in the literature.
Engagement of Oil Immersed Multi-Disc Clutches
Authors: Jacobson Bengt
Published: March 2021

Oil immersed clutches are often treated without respect to the oil being present, i.e. the torque is assumed to be a pure dry friction torque, directly controlled by the actuating force. However, during the engagement this is sometimes not enough. The oil film acts in two ways: Firstly, the oil has to be squeezed out before dry friction can be developed. Secondly, before the friction surfaces have reached contact, the torque is viscous. This work proposes equations that take these phenomena into account. A simple model for the transition from viscous to dry friction is used. Compensation for grooves in the friction surface is made. Also the hydraulic actuating equipment (piston, return spring, orifice etc.) is modelled. Simulation results are verified by experiments.
A Generation Mechanism of Aerodynamic Sound of Spur Gears
Authors: Houjoh Haruo , Umezawa Kiyohiko
Published: March 2021

It was already discovered that a pair of spur gears generates the tooth mesh frequency sound due to a fluctuating air flow. This sound is generated independently from the sound corresponding to mechanical vibration. In this study, to clarify the detailed generation process of the sound including the Level Trough which is one of specific feature of sound emission, experimental investigations were performed. It has been found that there is two sorts of sound; one is placed at the middle in the mesh end region, and is point source which appears when the air flow velocity reaches a critical speed. The other one is placed at both face end surfaces, whose magnitude decreases by either shortening center distance or shallowing tooth root spaces even though the air flow velocity increases. By assuming that the air flow comes from the pumping through the mesh process, a general explanation for the sound generation is presented.
Bearing Vibration and Oil Film Thickness in Relation to Sphericity of Bearing Steel Balls
Authors: Itoigawa F. , Nakamura T. , Funabashi K.
Published: March 2021

The relationship between the bearing vibration and the sphericity of the steel balls used for ball bearings is experimentally investigated in consideration of the oil film in between the steel balls and raceways. The experiments are carried out on angular contact ball bearings (7208C and 7010C) under only thrust load. First, it is confirmed that the oil film thickness, which is measured on this bearing, virtually agrees with the value calculated by EHL theory. And even if there exists a considerably large error in the ball shape, it does not always necessarily rupture the oil film if it is sufficiently thick. Second, in a simple two-bearing-shaft system, the even-order undulation of form error of ball, especially, second-order undulation, can cause bearing vibration. Furthermore, when the ball has a three-dimensional shape like a rugby ball, with elliptical cross-sections, the ball determines its own rotational axis.
Optimization of Involute Gear Tooth Profile Modification for Tooth Scoring Reduction
Authors: S'roda Prokop , Huston Ronald L.
Published: March 2021

This paper presents a method for determining optimum involute tooth profile modifications to reduce scoring and to increase load bearing capacity. The method is based upon Bloks theory of lubrication and wear. The method leads to design charts incorporating common geometrical gearing parameters. An example is presented.
Aspects in the Shape Optimization Using Brittle and Ductile Materials
Authors: Eschenauer H. A. , Vietor T.
Published: March 2021

The use of advanced materials will increasingly gain importance in future developments of constructions in mechanical, electrical and civil engineering. For this reason, the material behaviour in particular has to be considered when finding optimal layouts for components. Here, the different failure mechanisms of the applied materials must be taken into consideration. This paper presents a comparison between conventional, ductile materials and brittle ceramics as an example of an advanced material. In order to find a failure criterion which is characteristic of the material, stochastic models of the defects determining the failure of ceramic materials have been included. A strong variation in the calculated optimal design shows that an accurate consideration of the material behaviour and its mathematical description is important for the results to be found. The use of conventional stress criteria does not suffice for ceramic materials.
The Explicit Approximation Method for 2-D Shape Optimization Under Displacement Constraint
Authors: Hsu Yen-Liang , Sheppard Sheri D. , Wilde Douglass J.
Published: March 2021

The Explicit Approximation Method for 2D shape optimization under displacement constraint is presented. This is a zeroth order sequential approximation method. The basic idea is to use mechanical knowledge instead of purely numerical gradient information to form an explicit approximation to the implicit constraint. Design examples are presented to show that the displacement constraint usually has a good explicit approximation in 2D problems, and a good and feasible, if not theoretically optimum, design can be found very efficiently by the Explicit Approximation Method using only zeroth order information.
A Knowledge Based System for Intelligent Process Planning
Authors: Yu Jin , Liou F. W. , Tong Zhongfang , Sun Yueming
Published: March 2021

Knowledge extraction and representation are the two most important problems to build up expert systems. This paper describes an example of a knowledge based prototype Hi-KJBIPP, which is designed in a hierarchical architecture to express different levels of machining knowledge for complex box-type workpieces. Production systems and frames are both used as knowledge representation methods in Hi-KBIPP. A production rule system is used to represent top levels of knowledge, in which the control strategies that consist of priority classification, priority execution, and context restriction are designed to decide the first rule to be executed when several rules are of the same qualification. Frames are used to represent the information of machining procedures. A particular frame system is used in Hi-KBIPP which provide multi-dimension frame, similarity network, and associate-network to handle and compile knowledge.
Design of a Non-Homogeneous Annular Disk Under Pressure Loadings
Authors: Gau Chung-Yun , Manoochehri Souran
Published: March 2021

A method for the design of non-homogeneous, variable-thickness, annular disks under internal and external pressures satisfying Tresca yield criterion is presented in this paper. The effects of varying the disk thickness and stiffness properties to achieve a fully stressed design are investigated. Analytical solutions for distributions of Young’s modulus and disk thickness variations have been developed for the case of fully stressed designs. Examples are given for three different cases, namely, constant thickness with variable Young’s modulus, variable thickness with constant Young’s modulus, and variable thickness with variable Young’s modulus. In the last case, due to the existence of many alternative solutions, optimal design techniques have been utilized and the results are presented.
Discrete Optimal Design Formulations: Application to Gear Train Design
Authors: Pomrehn Leonard P. , Papalambros Panos Y.
Published: March 2021

The use of discrete variables in optimal design models offers the opportunity to deal rigorously with an expanded variety of design situations, as opposed to using only continuous variables. However, complexity and solution difficulty increase dramatically and model formulation becomes very important. A particular problem arising from the design of a gear train employing four spur gear pairs is introduced and formulated in several different ways. An interesting aspect of the problem is its exhibition of three different types of discreteness. The problem could serve as a test for a variety of optimization or artificial intellegence techniques. The best known solution is included in this article, while its derivation is given in a sequel article.
Infeasibility and Non-Optimality Tests for Solution Space Reduction in Discrete Optimal Design
Authors: Pomrehn Leonard P. , Papalambros Panos Y.
Published: March 2021

Techniques to be employed for nonlinear design optimization with discrete variables are studied in the context of a particular problem arising from the design of a gear train. The mathematical model formulation was presented in an earlier article. In this sequel, a solution derivation is described, patterned as a multistage process. After certain reformulation and relaxation, a variety of infeasibility and non-optimality tests are performed, greatly reducing the size of the space containing the global optimum. Methods used to investigate the remaining space do not guarantee a global optimum, but could be replaced by more costly methods that do provide such guarantees. A global infimum is generated, bounding any improvements on the best known solution.
Optimum Design of Rotational Wheel and Casing Structures Under Transient Thermal and Centrifugal Loads
Authors: Hattori T. , Toriya H.
Published: March 2021

Transient thermal and centrifugal loads on turbomachinery rotors have increased with recent increases in gas temperatures and tip speeds. Rotor weights must be decreased to improve rotor dynamics and to reduce bearing loads. Moreover, blade tip clearance must be decreased to improve aerodynamic efficiency. An optimum design technique offering the lightest possible wheel shape under specified stress and clearance limits is therefore required.

This paper introduces an optimum design system developed for turbo-machinery rotors. Sequential linear programming is used in the optimizing process, and non-steady-state thermal analyses of wheels and casings are performed by numerically analyzing multi-ring models. Stress and deformation analyses of these wheels and casings are performed by using Donath’s method with the same multi-ring model. This optimum design program is applied to the design of multistage axial flow compressor wheels.
An Alternative Approach to Mechanical Advantage for the Analysis of a Multiple-Input Multiple-Output Mechanical Device
Authors: Ogot M. M. , Gilmore B. J.
Published: March 2021

The design efficiency of mechanical systems has traditionally been measured via mechanical advantage (MA) which relates the amount of force exerted at the output to the corresponding force applied at the input. MA has been confined to single-input single-output devices, and only recently to single-input multiple-output port devices. This paper presents an alternative approach to MA. The classical definition of MA required the input force to do work on the mechanism, and the output force to be worked on by the mechanism. However this may cause problems where the external loads flip back and forth between doing work to and being worked on by the mechanism at different points in the cycle. This paper overcomes this difficulty by considering the input force as that applied by the mechanism actuator, and the output force to be the external or applied load. With these definitions, a general expression for MA applicable to multiple-input, multiple-output port mechanisms is presented.
Attributed Graph Model for Geometric Tolerancing
Authors: Shah Jami J. , Zhang Bing-Chun
Published: March 2021

The development of a face-based attributed graph structure for modeling geometric tolerances is described here. The structure, designated as the DTF graph, provides an integrated view of the dimensioning scheme, dimensions, tolerances, features, and datums. In the current version of the DTF model, all ANSI Y14.5M tolerance classes are supported, except profile tolerances. Edge related tolerances (straightness, circularity) are supported by derived face intersections. Other tolerances, and datum reference frames, are supported as face attributes or attributes of the DTF graph. The tolerance model is compatible with commonly used hybrid CSG-Brep solid modelers and has the property of uniqueness for any dimensioning scheme. Applications of the DTF Graph include: detection of over and under-constrained dimensions, automatic re-dimensioning if the designer changes the dimensioning scheme, and automatic discovery of dimension-tolerance stack-up loops.
Geometric Design and Fabrication of Developable Bezier Surfaces
Authors: Bodduluri R. M. C. , Ravani B.
Published: March 2021

In this paper we study Computer Aided Geometric Design (CAGD) and Manufacturing (CAM) of developable surfaces. We develop direct representations of developable surfaces in terms of point as well as plane geometries. The point representation uses a Bezier curve, the tangents of which span the surface. The plane representation uses control planes instead of control points and determines a surface which is a Bezier interpolation of the control planes. In this case, a de Casteljau type construction method is presented for geometric design of developable Bezier surfaces. In design of piecewise surface patches, a computational geometric algorithm similar to Farin-Boehm construction used in design of piecewise parametric curves is developed for designing developable surfaces with C2 continuity.

In the area of manufacturing or fabrication of developable surfaces, we present simple methods for both development of a surface into a plane and bending of a flat plane into a desired developable surface. The approach presented uses plane and line geometries and eliminates the need for solving differential equations of Riccatti type used in previous methods.

The results are illustrated using an example generated by a CAD/CAM system implemented based on the theory presented.
Numeric-Symbolic Approach for Dynamic Modelling of Robotic Manipulators
Authors: Fan Shou-wen , Xu Liju , Chen Yong
Published: March 2021

A simple numeric-symbolic method for dynamic modelling of robotic manipulators is proposed in this paper. Problem of deriving model matrix elements is transformed into problem of solving for driving force and driving torque under specified condition by recursive dynamic equations. Expressions of reaction force in arbitrary joint in numeric-symbolic form are also derived. Corresponding software which can recognize and manipulate symbols is developed and can be used to generate model and real-time code of robotic dynamics.
Parametric Design of Low Lateral Force Rollers for Belt Loop Drives
Authors: Hoeltzel David A. , Quadracci H. Richard , Castelli Vittorio
Published: March 2021

Belt loops supported by rollers commonly appear in xerographic type copying machines. Recently, rollers have been designed with special mechanical features employing a series of stacked annular discs mounted on a solid drive shaft. This configuration reduces the transverse forces acting on the belt due to edge guidance, and provides a method of belt control which eliminates the need for costly active belt steering servo systems. Rollers of this type are referred to as low lateral force (LLF) rollers. The addition of these lateral load inhibiting features necessitates that the rollers be carefully scrutinized for buckling and deformation, thereby ensuring accurate belt control for high quality xerographic copying.

A parameterized finite element model of a LLF roll has been developed. The results acquired from the model are presented in dimensionless form in terms of the physical variables that describe the geometric parameters of the discs comprising the roller: thickness, inner and outer radii and belt contact angle. Dimensionless forms for the buckling belt tension and the circumferential and axial stiffnesses of the discs are also evaluated and displayed against the dimensionless geometric parameters, using contour plots for belt contact angles of 45°, 90°, 135° and 180°. These plots have been employed in practical design calculations for the sizing of LLF rolls.
Direct Differential Kinematics of Hybrid-Chain Manipulators Including Singularity and Stability Analyses
Authors: Xu Yong-Xian , Kohli Dilip , Weng Tzu-Chen
Published: March 2021

A general formulation for the differential kinematics of hybrid-chain manipulators is developed based on transformation matrices. This formulations leads to velocity and acceleration analyses, as well as to the formation of Jacobians for singularity and unstable configuration analyses. A manipulator consisting of n nonsymmetrical subchains with an arbitrary arrangement of actuators in the subchain is called a hybrid-chain manipulator in this paper. The Jacobian of the manipulator (called here the system Jacobian) is a product of two matrices, namely the Jacobian of a leg and a matrix M containing the inverse of a matrix Dk, called the Jacobian of direct kinematics. The system Jacobian is singular when a leg Jacobian is singular; the resulting singularity is called the inverse kinematic singularity and it occurs at the boundary of inverse kinematic solutions. When the Dk matrix is singular, the M matrix and the system Jacobian do not exist. The singularity due to the singularity of the Dk matrix is the direct kinematic singularity and it provides positions where the manipulator as a whole loses at least one degree of freedom. Here the inputs to the manipulator become dependent on each other and are locked. While at these positions, the platform gains at least one degree of freedom, and becomes statically unstable. The system Jacobian may be used in the static force analysis. A stability index, defined in terms of the condition number of the Dk matrix, is proposed for evaluating the proximity of the configuration to the unstable configuration. Several illustrative numerical examples are presented.
Direct Position Kinematics of the 3-1-1-1 Stewart Platforms
Authors: Husain Muqtada , Waldron Kenneth J.
Published: March 2021

In this work, a closed form solution for the direct position kinematics problem of a special class of Stewart Platform is presented. This class of mechanisms has a general feature that the top platform is connected to the six limbs at four locations. Three limbs connect at one location and the remaining limbs connect to the top platform singly at three separate locations. The base platform is connected at six different locations as is the case in the general platform. This particular class of mechanism is termed as 3-1-1-1 mechanism in this paper. It has been shown that there are a maximum of sixteen real assembly configurations for the direct position kinematics problem. This has been verified using a geometric argument also. The numerical example solved in this paper demonstrates that it is possible to obtain a set of solutions which are all real.
Inverse Kinematics of General 4R2P, 3R3P, 4R1C, 2R2C, and 3C Serial Manipulators
Authors: Kohli Dilip , Osvatic Michael
Published: March 2021

This paper presents a solution to the inverse kinematics problem for 4R2P, 3R3P, 4R1C, 2R2C and 3C manipulators of general geometry. The method used to solve these is based on a technique recently presented by the authors for solving the inverse kinematics of general 6R and 5R1P manipulators. In the 6R and 5R1P cases, the method initially starts using 14 linearly independent equations where as for the 4R2P, 3R3P, 4R1C, 2R2C and 3C manipulator only 3, 6, 7 or 10 linearly independent equations are required, depending on the case. Through the use of a linearization and dialytic elimination method all 4R2P, 3R3P, 4R1C, 2R2C and 3C cases are reduced to equating to zero the determinant of a matrix whose elements are linear in the tangent of a half angle of a joint variable. The size of this matrix is (8 × 8) for all 4R2P manipulators, (2 × 2) for all 3R3P and 3C manipulators, (16 × 16) for 4R1C manipulators, (4 × 4) for RCRC and CRCR manipulators and (8 × 8) for the remaining 2R2C manipulators providing 8th, 2nd, 16th, 4th and 8th degree inverse kinematic polynomial respectively. Thus, the determinant equated to zero gives us the characteristic equation of the degree expected. The unique form of the matrix allows us to obtain the solution by solving an eigenvalue problem. Many variations of the 4R2P, 3R3P, 4R1C, 2R2C and 3C manipulators are presented and the solution methodology is illustrated by several numerical examples.
Design Improvement of Manipulators by Minimizing Shaking Force/Moment and Driving Torques
Authors: Husain Muqtada , Mallik Akhtar K. , Ghosh A.
Published: March 2021

In this work, an algorithm for design improvement of open loop manipulators, after allowing for the necessary trade-offs among the maximum shaking force, shaking moment and the driving torques is presented. The improved design is attempted by only proper mass distribution of the links for the given kinematic structure and link masses. A min-max optimization problem, considering the worst configuration, is formulated via closed form expressions of the dynamical quantities derived by using Newton-Euler approach. The procedure, though applicable in general, is illustrated through the design of the arm structure of a PUMA 560 manipulator. This developed procedure will also be very helpful in the mechanical design of any new manipulator arm.
Optimal Synthesis and Analysis of a New Leg Mechanism: The Planetary Gear Leg
Authors: Chen Ning-Xin , Song Shin-Ming
Published: March 2021

The leg mechanism of a walking machine has a strong influence on the performance of the machine. A successful leg mechanism should be energy efficient, compact in size, strong and simple. In order to achieve good energy efficiency, a walking machine leg should be able to generate an exact or approximate straight line at the foot with only one driving actuator. This paper deals with the synthesis and analysis of a new leg mechanism — the planetary gear leg mechanism. Four types of planetary gear legs are studied. By the SUMT optimization method, a 20 inch tall leg is able to generate an approximate straight line trajectory with a maximum deviation of 0.12805 inches in a 20 inch stroke. The direct and inverse kinematics and velocities of the legs are analyzed. Also, the distribution of actuator force/moment during walking are studied. The results show that this leg design has great potential to be used as a practical walking machine leg.
The Dynamic Equations of Motion and Actuation Scheme for the Tetrahedron Based Variable Geometry Truss Manipulator
Authors: Sarma Radha , Kramer Steven N. , Ramamurti V.
Published: March 2021

The Variable Geometry Truss Manipulator (VGTM) is a truss structure composed of tetrahedron elements stacked upon each other. Although this manipulator is geometrically different from a serial link manipulator, it is kinematically equivalent to the serial link manipulator whereby the difference in construction lies in its 120° twist angles instead of the more common 0° or 90°. A study of the dynamic behavior of a manipulator is important for simulation of the motion of the manipulator, designing suitable control equations and for evaluating the kinematic design and structure of the manipulator. In this paper the dynamic equations of motion have been derived for the VGTM. The different components of the torques have been computed using the Lagrange-Euler equations with the intention of studying the contributions of each term. In addition, two actuation schemes for the VGTM have been studied: actuation at each joint axis and actuation at the apex of each triangular element. The motor requirements for each scheme have been obtained and compared. A case study has been performed for a typical trajectory this manipulator.
Geometrical Properties of Modelled Robot Elasticity: Part II — Center of Elasticity
Authors: Lipkin Harvey , Patterson Timothy
Published: March 2021

The elastic characteristics of many robot systems can be modeled by a 6 × 6 stiffness or compliance matrix. Several new and important results are presented via screw theory: i) A generalized center-of-elasticity is proposed based on Ball’s (1900) principal screws and its properties are investigated, ii) If a compliant axis exists, it is shown to pass through the center. iii) The perpendicular vectors from the center to the wrench-compliant axes are coplanar and sum to zero. A similar result holds for the twist-compliant axes, iv) Linear and rotational properties are characterized by dual ellipsoids in three-dimensional space. These elements simplify the understanding of complex elastic properties.
Path Generation for Two Cooperative Puma Robots
Authors: Chen Jau-Liang , Duffy Joseph
Published: March 2021

This paper describes the development of generating collision-free paths for a pair of cooperative PUMA robots as their end effectors grasp a workpiece in an obstacle-strewn environment. After the initial and goal positions of the wrist center are specified, a collision-free path for this pair of manipulators to move the workpiece safely to the final destination is generated. The algorithm is demonstrated via computer graphics animation on a Silicon Graphics IRIS 4D/70GT workstation.
Analysis and Synthesis of Frictionless Planar Grasping in an Image Space
Authors: Dai J. S. , Kerr D. R.
Published: March 2021

Theories are presented which describe the grasping of an arbitrary planar object using frictionless point contacts. The theories are based on screw algebra and line geometry, and allow the mapping of the contacts onto an image space, with the study of the necessary relationships between the contacts and the determination of whether these contacts can form a successful grasp. An identical mapping is also used for the relevant surface properties of the shape of the object to be grasped, so that synthesis of grasps can be achieved. Examples of the application of these theories are given.
Determination of the Singularity Loci of Spherical Three-Degree-of-Freedom Parallel Manipularors
Authors: Gosselin Clément M. , Sefrioui Jaouad
Published: March 2021

In this paper, an algorithm for the determination of the singularity loci of spherical three-degree-of-freedom parallel manipulators with prismatic atuators is presented. These singularity loci, which are obtained as curves or surfaces in the Cartesian space, are of great interest in the context of kinematic design. Indeed, it has been shown elsewhere that parallel manipulators lead to a special type of singularity which is located inside the Cartesian workspace and for which the end-effector becomes uncontrollable. It is therfore important to be able to identify the configurations associated with theses singularities.

The algorithm presented is based on analytical expressions of the determinant of a Jacobian matrix, a quantity that is known to vanish in the singular configurations. A general spherical three-degree-of-freedom parallel manipulator with prismatic actuators is first studied. Then, several particular designs are investigated. For each case, an analytical expression of the singularity locus is derived. A graphical representation in the Cartesian space is then obtained.
A New Approach to Type Synthesis of Spatial Robotic Mechanisms
Authors: Malik Akhtar N. , Kerr D. R.
Published: March 2021

This paper presents a new approach for carrying out the type synthesis of spatial parallel platform-type mechanisms, used as robot manipulators. It takes into account the total mobility of the system and the partial mobility of its sub-mechanisms. The paper also provides the necessary and sufficient conditions for the mechanisms to function with specified end-effector freedoms, which are described in two theorems. The total number of possible mechanisms with given mobility and structure are tabulated. The work is based on a modified Grübler mobility criterion and also on the consideration of kinematic restraints.
Path Planning for an Articulated Transporter/Manipulator System
Authors: Chiang Shih-chien , Crane Carl D. , Duffy Joseph
Published: March 2021

This work addresses the three dimensional path planning for an Articulated Transporter/Manipulator System (ATMS) in a given working environment. A vertical motion capability provides the ATMS a new ability which can be used to advantage in the generation of collision free paths. It also complicates the path planning process, however, by not being constrained to a 2D environment. A hierarchical structure of path planning is developed to decompose the three-dimensional path planning problem into several two-dimensional sub-problems.
Real Time Trajectory Modification Using a Closed Form Solution
Authors: Hummels Michael R. , Cipra Raymond J.
Published: March 2021

An on-line trajectory modification and path planning strategy is developed which will allow a robot to respond in an efficient manner to real time sensory input. The approach developed here eliminates the need for solving many equations by developing a closed form algorithm. It uses two fourth order curves for the transition phases with a constant velocity section in between. Although this is done by providing additional constraints to the curve, it makes the problem of determining the trajectory much easier to solve, while providing continuous higher derivatives. It also provides a safe and efficient way of modifying trajectories based on the robots joint rate limits, joint acceleration limits, jerk limits, and desired time interval between trajectory modifications for a 4-1-4 trajectory. This method involves the solution of one second order equation and is directed toward real time applications.
Optimal Trajectory Resolution for the Coordination of Two Robots in Contact Operations
Authors: Tabarah E. , Benhabib B. , Fenton R. G. , Hexner G.
Published: March 2021

A new method is presented for the optimal coordination of a two-robot system performing contact operations. One of the robots carries a tool and performs the specific contact operation on a workpiece which is grasped and maneuvered by the second robot. The two robots move simultaneously relative to each other so that the tool maintains contact with the workpiece while moving along its prescribed trajectory at a constant speed. This prescribed trajectory, which is specified with respect to the workpiece frame, is thus resolved into a pair of conjugate trajectories, one for each robot, and specified in the world coordinate frame. This resolution process does not yield a unique solution, i.e. there exist an infinity of conjugate-trajectory pairs corresponding to a given tool trajectory. This paper presents a technique for resolving the original tool trajectory, where the robots’ conjugate trajectories are parameterized using polynomial functions. A method is then developed for selecting the optimal pair of conjugate trajectories on the basis of minimizing a given choice of cost function. This optimization is further enhanced by coupling it to a procedure for selecting the optimal layout of the robots within the workcell, resulting in the best possible solutions. Numerical simulation results support the validity of the proposed technique.
An Application of Planar Two Parameter Motion Curvature Theory to the Trajectory Generation Problem of a Two-Link Manipulator
Authors: Stanišić M. M. , Lodi K. , Pennock G. R.
Published: March 2021

This paper illustrates a new application of planar curvature theory to the geometric problem of trajectory generation by a two-link manipulator. The theory yields the instantaneous speed ratio, and the rate of change of the speed ratio, which correspond to the geometry of a desired point trajectory. Separate from the purely geometric speed ratio problem (i.e. the coordination problem) is the time based problem of controlling the joint rates in order to move with the specified path variables.
On The Kinematic Design of Manipulators for Limited Access Workspaces (LAWS)
Authors: Shooter Steven B. , Reinholtz Charles F. , Dhande Sanjay G.
Published: March 2021

Robotic manipulators for Limited Access WorkSpaces, or LAWS manipulators, must operate in unalterable, confined environments accessed through constrictive portals. The characteristics of these manipulators distinguish them from currently accepted classes of industrial robots and field robots and evoke a particular design strategy. Special consideration must be given to the ability of the LAWS manipulator to service a target workspace while constrained within the boundaries of a confined environment. Applications for robots that can operate in limited access workspaces exist in the nuclear, construction, mining, and medical industries, among others. This paper characterizes LAWS manipulators and develops a strategy for their kinematic design. This strategy is then applied to the design and analysis of a typical LAWS manipulator.
Determination of the Workspace of the 3-DOF Double-Octahedral Variable-Geometry-Truss Manipulator
Authors: Arun V. , Padmanabhan Babu , Kolady Krishnan , Reinholtz Charles F.
Published: March 2021

This paper presents methods to determine the workspace of the 3-DOF double-octahedral variable-geometry-truss manipulator (VGTM). These methods take advantage of some of the geometric properties inherent in octahedral VGT construction and define regions in space whose intersection results in the workspace of the manipulator. This approach of obtaining a ‘common volume’ can be extended to other parallel manipulators.
Push-Pull Pair of Single Action Mechanisms to Preload Strut and Node Joints in the Robotic Assembly of Structures in Space
Authors: Brewer W. V.
Published: March 2021

When strut and node components are used for truss construction or repair, an assembly problem occurs if a strut must fit between nodes whose separation distance is either more or less than the design specification. In such circumstances two actions would permit continued assembly:

1. Change strut length

2. Move the nodes.

Variable length struts fit between nodes and (or) move them. They are preloaded at the joint against a reference length in an attempt to maintain the desired dimension. As a by-product they either pull the nodes together or push them apart. Most cannot do both, and are therefore characterized as “single action”; those that can do both are “double action”.

Double action mechanisms are currently being used for robotic truss assembly because they solve the above stated crucial problem in both directions. Single action mechanisms tend to exhibit superior performance in all other categories. They benefit from the attributes that accompany their simplicity.

The titled concept combines the major advantage of double action with the simplicity of single action. This is demonstrated with an example.
Full-Wave Bi-Directional Rotation-Rectifier to Assist Robotic End-Effectors in the Automated Assembly of Large Truss Structures in Space
Authors: Brewer W. V.
Published: March 2021

In 1987 work was initiated on the Automated Structural Assembly Laboratory (ASAL) at NASA/LaRC to demonstrate the feasibility of robotic construction in orbit. To move itself as the structure grows, the robot is mounted on a carriage that traverses a beam which moves longitudinally, similar to a gantry crane. Gantry motions will be operated by the self-sufficient robot with its wrist roll motion. Interfaces for the robot at each gantry motor shaft are provided for that purpose. Wrist roll is limited by the large and growing number of wires that must communicate thru the wrist joint to connect the end-effector to power, sensory devices, and computation services. Rotation-Rectifiers applied to robot mobility simplify the end-effector to motor shaft interface, reduce the number of interface operations that must be performed, and convert oscillating robot wrist roll motions to continuous rotation in either direction.
Forward Kinematics of the General 6-6 Fully Parallel Mechanism: An Exhaustive Numerical Approach via a Mono-Dimensional-Search Algorithm
Authors: Innocenti C. , Parenti-Castelli V.
Published: March 2021

A new numerical method for the solution of the direct position analysis of the six d.o.f. fully parallel mechanism with general geometry, often referred to as generalized Stewart platform mechanism, is presented. The main feature of the method, making it attractive with respect to the methods available in the literature, is the ability to find out all the real solutions of the direct position analysis. The effectiveness of the new algorithm relies upon the solution of only one equation in one unknown. That equation is strictly representative of the problem, i.e., it is free from extraneous roots and every solution of the direct position analysis entails the existence of a root for the equation. A case study is reported.
Workspace of Beetle Body As a Function of Foot Position
Authors: Foo C. K. , Fichter E. F. , Fichter B. L.
Published: March 2021

Body workspace with foot positions fixed was examined for 16 sets of foot positions at 3 body heights using a simulation model of a darkling beetle. Body orientation was held constant and all foot positions were symmetrical about the bilateral symmetry plane. Horizontal plane sections of body workspace were plotted.

Maximum body workspace areas were nearly always at the observed normal resting height of the beetle. Maximum body workspace areas occurred with feet in the relative positions they have when near the centers of their respective workspaces. Changing positions of front and hind feet had much more influence on shape and area of body workspace than changing positions of middle feet. Conclusions from this study raise important considerations for the design of walking machines.
Design and Motion Planning of Multi-Limb Robotic Systems: The Force-Workspace Approach
Authors: Madhani Akhil , Dubowsky Steven
Published: March 2021

A method, called the Force Workspace (FW) approach, is presented for the design and motion planning of mobile multi-limb robotic systems which must as part of their tasks apply large forces over large ranges of motion. These systems will be limited by actuator force/torque saturation limits, system-environment force and moment constraints such as friction, and kinematic joint limits. The FW can be used for the quantitative design of such systems and enables motions to be planned to perform tasks without violating the above constraints. Examples of FW based design and planning are given for a robotic climbing machine.
The Mechanical Design of a Parallel Actuated Joint for an Articulated Mobile Robot
Authors: Ridgeway Shannon , Crane Carl D. , Adsit Phillip , Harrell Roy
Published: March 2021

The suitability of the parallel planar actuator (PPA) to application in an articulated mobile robot is evaluated. Examination of several joint actuation schemes is presented along with the introduction of the PPA. The PPA has a high joint torque generating capacity and a distributed structure that leads to a light, stiff mechanism. A segment of an articulated mobile robot with the kinematic configuration of the PPA has been designed and fabricated. The design process is outlined and the major components are described. The mechanism is operational and meets major design criteria.
A Derivation of the Pole Curve Equations in the Projective Plane
Authors: Brady Michael H. , Peterson Steven W.
Published: March 2021

The traditional four-position method of mechanism synthesis focuses on the poles corresponding to four displacements. From these poles arise equations for the center-points and circle-points of possible four-bar linkages. However, if one of the poles is infinite (the associated displacement is a pure translation), the established derivations for the pole curve equation break down. This problem is rectified by expressing the pole curve equation in the projective plane, because all points, including points at infinity, have finite homogeneous coordinates. In Part I of this paper, this form of the pole curve equation is applied to opposite-pole quadrilaterals formed by four finite poles. This projective derivation is an analytic expression of Alt’s graphical construction of the pole curve. The pole curve is the intersection of a pair of projective pencils of circles (one pencil for each side of a pair of opposite sides in the opposite-pole quadrilateral) which are defined by the homogeneous coordinates of the poles. The resulting equation for the pole curve is a function of the locations of the poles and of the orientation of one opposite side of the opposite-pole quadrilateral relative to the other.
A Straight-Line Mechanism and its Application in Vehicles
Authors: Zhang S. J. , Sanger D. J.
Published: March 2021

This paper describes a mechanism which generates straight-line motion segments and which is especially appropriate for use as the basis for a walking wheel in various kinds of vehicles. The straight-line motion capability, with multiple legs in the wheel, is exploited to ensure that the height of the wheel centre above ground is maintained constant. Thus, the wheel can be used on hard surfaces as well as on soft surfaces, with a suitable foot attached to the leg to ensure that an appropriate level of ground pressure is maintained.