# A series-parallel hybrid mechanism analysis for a bio-inspired piping inspection robot

Swaminath Venkateswaran, Damien Chablat

► To cite this version:

Swaminath Venkateswaran, Damien Chablat. A series-parallel hybrid mechanism analysis for a bio-inspired piping inspection robot. Multidisciplinary Biomechanics Journal, 2025, 50th congress of the., 10.46298/mbj.16185. hal-05191737v2

HAL Id: hal-05191737

https://hal.science/hal-05191737v2

Submitted on 23 Oct 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>
# A series-parallel hybrid mechanism analysis for a bio-inspired piping inspection robot

Swaminath Venkateswaran<sup>a*</sup>, Damein Chablat<sup>b, c</sup>

a De Vinci Research Center, De Vinci Higher Education, Paris, France

b École Centrale Nantes, Nantes Université, CNRS, LS2N, UMR 6004 F-44000 Nantes, France

c Research Center for Industrial Robots Simulation and Testing, Technical University of Cluj-Napoca, Memorandumului 28 400114 Cluj-Napoca, Romania

* Corresponding author: swaminath.venkateswaran@devinci.fr

Received date: 06/04/2025

Accepted date: 27/06/2025

Publication date: 27/10/2025

Keywords: series-parallel mechanism, tilt angles, experiments, bio-inspired

© 2025 The Authors

Licence CC-BY 4.0

Published by Société de Biomécanique

## 1. Introduction

Parallel robots or Parallel Kinematic Machines (PKM) offer several advantages when compared to their serial counterparts such as low mass/inertia properties, higher structural stiffness and better accuracy. Their limited workspace however proves to be a disadvantage when compared to the serial robots. Recent research works have come up with the solution of hybrid mechanisms where one or more parallel robots are stacked over the other. This proves to be advantageous as the resulting mechanism could benefit from better accuracy from the parallel robot and larger workspace from the serial robot (Carbone and Ceccarelli 2004). In this paper, we present a series-parallel spherical mechanism. The mechanism consists of two 3-SPS-U architectures stacked on top of the other (Venkateswaran et al. 2023, Venkateswaran and Chablat 2023). The mechanism is analyzed using the theory of Tilt & Torsion (Bonev et al. 2008) instead of Euler angles in order to solve the singularity problems and understand the tilt limits. Experiments are then carried out to understand the tilt limits of the mechanism. It was observed that due to frictional factors and cable tension, higher noise with some errors was observed between the desired and measured values. The main purpose of this hybrid mechanism is to deploy the architecture for a bio-inspired piping inspection robot to overcome T-unions or junctions (Venkateswaran et al. 2019). The proposed 3-SPS-U hybrid mechanism coupled with the piping inspection robot helps mimic an elephant trunk model.

## 2. Analytical Modeling

The modeling of the 3-SPS-U hybrid mechanism is presented in this section. An overview of the mechanism is presented in Fig. 1. (a) in Section-3. The base mounting points given by vector **b**, the intermediate mounting point given by vector **c** and the end-effector mounting point given by vector **d** are given by the equations:

$$b_{i+1} = [r_f \cos(\frac{2\pi i}{3}) r_f \sin(\frac{2\pi i}{3}), -r_f h]^T, c_{i+1} = E * [r_f \cos(\frac{2\pi i}{3}) r_f \sin(\frac{2\pi i}{3}) r_f h]^T \\ d_{i+1} = F * c_{i+1}, i = 1,2,3$$

The matrices **E** and **F** are transformation matrices that are used to map between the base and end-effectors. The parameters $r_f$ and $h$ were optimized in Venkateswaran and Chablat 2023, according to the dimensions of the piping inspection robot. Singularity analysis is then carried out using the Cylindrical Algebraic Decomposition (CAD) algorithm in Maple software to identify the theoretical tilt limits of the architecture, which are given below in Table 1.

The angles $\eta$, $\phi$ and $\zeta$, $\psi$ are the tilt angles of Stage-1 and Stage-2 of the mechanism in Euler space. The angles $\alpha$, $\delta$ are the tilt angles of each stage and $\beta$ is the common azimuth of the mechanism in the Tilt & Torsion space respectively.

## 3. Experiments

A simple experimental platform was constructed in laboratory as shown in Fig. 1. (a). The mechanism is
actuated through three DC motors. The EtherCAT module was used to actuate the system. A static modeling was carried to generate a circular trajectory. The maximum tilt angles was found to be around 0.6 radians for the overall module. The error percentage between the measured and desired values remained low, at around 0.014 %. However, due to slackening of cable and redundancy, there were some disturbances observed in the velocity profile. The error percentage was found to be around 0.5 %. The results of the experiments with the position and velocity profiles are shown in Fig. 1. (b). An overview of the application of this mechanism with the bio-inspired piping inspection is shown in Fig. 1. (c), with the stacked tensegrity structures. The entire assembly resembles an elephant trunk while going through a 90-degree bend and the entire robot supported by the tensegrity structures helps in overcoming pipe bends or T-unions.

<table><caption>**Table 1.** Theoretical tilt limits for the 3-SPS-U hybrid mechanism in radians.</caption><thead><tr><th>Motion type</th><th>η</th><th>φ</th><th>ζ</th><th>ψ</th></tr></thead><tbody><tr><td>Tilt</td><td>0</td><td>0 → π/6</td><td>0</td><td>0 → π/6</td></tr><tr><td>Circular</td><td>asin(β)</td><td>acos(β)</td><td>δsin(β)</td><td>δcos(β)</td></tr><tr><td>Tilt</td><td>0</td><td>π/6 → 0</td><td>0</td><td>π/6 → 0</td></tr></tbody></table>

## 4. Conclusions

In this article, we studied the design and actuation strategy of a 3-SPS-U type series-parallel hybrid mechanism. Theoretical analysis from our earlier analysis proved that each stage can offer 30 degrees (π/6 radians), resulting in an overall 60 degrees tilt from the hybrid model. For the experiments, we considered a value well within this limit of around 15 degrees. The circular trajectory was performed as this approach is essential for the piping inspection robot especially when it encounters a 90-degree bend. After overcoming a bend or a junction, the circular trajectory can be performed to realign the axis of the robot with the axis of the pipeline. During experiments, the overall error in position was highly satisfactory, thanks to the efficiency of the PID controller employed. However, due to slackening of cables, noise was observed in the velocity profile. At present, we are working on resolving

this by preloading the mechanism, which will ensure good tension in the cables during operation. Following that, the stacked mechanism will be deployed with the existing piping inspection robot in order to perform experiments within curved pipelines.

<figure><img src="image_2.png" /></figure>

<figure><img src="image_3.png" /><figcaption>**Figure 1.** (a) The experimental platform, (b) results from experiments, (c) the bio-inspired robot with the stacked tensegrity models.</figcaption></figure>
**Conflict of Interest Statement**

None.

**Contributor Roles**

SV: Conceptualization, Methodology, Writing original draft; DC: Methodology, Funding acquisition, Validation, Writing-review & editing.

**References**

Carbone, G., & Ceccarelli, M. (2004). A stiffness analysis for a hybrid parallel-serial manipulator. *Robotica*, 22(5), 567–576. https://doi.org/10.1017/S0263574704000323

Venkateswaran, S., Chablat, D., & Creusot, D. (2023). Design and analysis of a series-parallel hybrid 3-SP SU Mechanism. In *IDETC/CIE Conference* (Vol. 87363, p. V008T08A006). ASME. https://doi.org/10.1115/DETC2023-115225

Venkateswaran, S., & Chablat, D. (2023). Mapping the tilt and torsion angles for a 3-SP SU parallel mechanism. *Robotics*, 12(2), 50. https://doi.org/10.3390/robotics12020050

Bonev, I. A. (2008). Direct kinematics of zero-torsion parallel mechanisms. In *2008 IEEE ICRA* (pp. 3851–3856). IEEE. https://doi.org/10.1109/ROBOT.2008.4543802

Venkateswaran, S., Chablat, D., & Boyer, F. (2019). Numerical and experimental validation of the prototype of a bio-inspired piping inspection robot. *Robotics*, 8(2), 32. https://doi.org/10.3390/robotics8020032