A geometrical formulation for the workspace of parallel manipulators

Russo, Matteo; Ceccarelli, Marco

Abstract

In study this paper, a geometric formulation is proposed to describe the workspace of parallel manipulators by using a recursive approach as an extension of volume generation for solids of revolution. In this approach, the workspace volume and boundary for each limb of the parallel manipulator is obtained with an algebraic formulation derived from the kinematic chain of the limb and the motion constraints on its joints. Then, the overall workspace of the mechanism can be determined as the intersection of the limb workspaces. The workspace of different kinematic chains is discussed and classified according to its external shape. An algebraic formulation for the inclusion of obstacles in the computation is also proposed. Both analytical models and numerical simulations are reported with their advantages and limitations. An example on a 3-SPR parallel mechanism illustrates the feasibility of the formulation and its efficiency.

• Journal Article Type: Article
• Acceptance Date: Nov 17, 2021
• Online Publication Date: Dec 13, 2021
• Publication Date: 2022-08
• Deposit Date: Jan 19, 2022
• Publicly Available Date: Jun 14, 2022
• Journal: Robotica
• Print ISSN: 0263-5747
• Electronic ISSN: 1469-8668
• Peer Reviewed: Peer Reviewed
• Volume: 40
• Issue: 8
• Pages: 2581-2591
• DOI: https://doi.org/10.1017/S0263574721001806
• Keywords: Computer Science Applications; General Mathematics; Software; Control and Systems Engineering
• Public URL: https://nottingham-repository.worktribe.com/output/7059294
• Publisher URL: https://www.cambridge.org/core/journals/robotica/article/geometrical-formulation-for-the-workspace-of-parallel-manipulators/74994126794BD4DB8A5A4DA33A9085CB