Singularity and workspace analysis of three isoconstrained parallel manipulators with schoenflies motion

Abstract

This paper presents the analysis of three parallel manipulators with Schoenflies-motion. Each parallel manipulator possesses two limbs in structure and the end-effector has three DOFs (degree of freedom) in the translational motion and one DOF in rotational motion about a given direction axis with respect to the world coordinate system. The three isoconstrained parallel manipulators have the structures denoted as {\mathrm{C}}_{\mathrm{u}}^{\mathrm{u}}{\mathrm{U}}_{\mathrm{w}}{\mathrm{H}}_{\mathrm{w}}-//-{\mathrm{C}}_{\mathrm{v}}^{\mathrm{v}}{\mathrm{U}}_{\mathrm{w}}{\mathrm{H}}_{\mathrm{w}}, {\mathrm{C}}_{\mathrm{u}}{\mathrm{R}}_{\mathrm{u}}^{\mathrm{u}}{\mathrm{U}}_{\mathrm{h}\mathrm{w}}-//-{\mathrm{C}}_{\mathrm{v}}{\mathrm{R}}_{\mathrm{v}}^{\mathrm{v}}{\mathrm{U}}_{\mathrm{h}\mathrm{w}} and {\mathrm{C}}_{\mathrm{u}}{\mathrm{P}}^{\mathrm{u}}{\mathrm{U}}_{\mathrm{h}\mathrm{w}}-//- {\mathrm{C}}_{\mathrm{v}}{\mathrm{P}}^{\mathrm{v}}{\mathrm{U}}_{\mathrm{h}\mathrm{w}}. The kinematic equations are first introduced for each manipulator. Then, Jacobian matrix, singularity, workspace, and performance index for each mechanism are subsequently derived and analysed for the first time. The results can be helpful for the engineers to evaluate such kind of parallel robots for possible application in industry where pick-and-place motion is required.

Key words： parallel manipulator; schoenflies motion; kinematics; singularity; workspace; performance index

Acknowledgements

The authors would like to thank Professor Chung-Ching Lee of National Kaohsiung University of Applied Sciences for his suggestions on this work.

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