On the Certification of the Kinematics of 3-DOF Spherical Parallel Manipulators
Abstract: This paper aims to study a specific kind of parallel robot: Spherical Parallel Manipulators (SPM) that are capable of unlimited rolling. A focus is made on the kinematics of such mechanisms, especially taking into account uncertainties (e.g. on conception & fabrication parameters, measures) and their propagations. Such considerations are crucial if we want to control our robot correctly without any undesirable behavior in its workspace (e.g. effects of singularities). In this paper, we will consider two different approaches to study the kinematics and the singularities of the robot of interest: symbolic and semi-numerical. By doing so, we can compute a singularity-free zone in the work- and joint spaces, considering given uncertainties on the parameters. In this zone, we can use any control law to inertially stabilize the upper platform of the robot.
- C. M. Gosselin, J. Sefrioui, and M. J. Richard, “On the Direct Kinematics of Spherical Three-Degree-of-Freedom Parallel Manipulators of General Architecture,” Journal of Mechanical Design, vol. 116, no. 2, pp. 594–598, 06 1994. [Online]. Available: https://doi.org/10.1115/1.2919419
- A. Shintemirov, A. Niyetkaliyev, and M. Rubagotti, “Numerical optimal control of a spherical parallel manipulator based on unique kinematic solutions,” IEEE/ASME Transactions on Mechatronics, vol. 21, pp. 1–1, 01 2015.
- I. Tursynbek and A. Shintemirov, “Infinite torsional motion generation of a spherical parallel manipulator with coaxial input axes,” 2020 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM), pp. 1780–1785, 2020.
- A. Lê, F. Rouillier, G. Rance, and D. Chablat, “Inertial Line-Of-Sight Stabilization Using a 3-DOF Spherical Parallel Manipulator with Coaxial Input Shafts,” in 11th International Symposium on Optronics in Defense & Security, Bordeaux, France, Jan 2024. [Online]. Available: https://inria.hal.science/hal-04483255
- ——, “On the Certification of the Kinematics of 3-DOF Spherical Parallel Manipulators,” Maple Transactions, vol. 3, 08 2023. [Online]. Available: https://doi.org/10.5206/mt.v3i2.15660
- D. Chablat, P. Wenger, and J.-P. Merlet, “An interval analysis based study for the design and the comparison of three-degrees-of-freedom parallel kinematic machines,” The International Journal of Robotics Research, vol. 23, no. 6, pp. 615–624, 2004.
- L. V. Kantorovich, “On Newton’s method for functional equations,” Functional Analysis and Applied Mathematics, vol. 59, no. 7, pp. 1237–1240, 1948.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.