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

doi:10.1007/s11465-012-0324-5

Front Mech Eng

2012, Vol. 7

Issue (2) : 163-187 https://doi.org/10.1007/s11465-012-0324-5

RESEARCH ARTICLE

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

Po-Chih LEE, Jyh-Jone LEE(

)

Department of Mechanical Engineering, Taiwan University, Taipei, China

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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 CuuUwHw-//-CvvUwHw, CuRuuUhw-//-CvRvvUhw and CuPuUhw-//- CvPvUhw. 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.

Keywords parallel manipulator schoenflies motion kinematics singularity workspace performance index

Corresponding Author(s): LEE Jyh-Jone,Email:jjlee@ntu.edu.tw

Issue Date: 05 June 2012

Cite this article:

Po-Chih LEE,Jyh-Jone LEE. Singularity and workspace analysis of three isoconstrained parallel manipulators with schoenflies motion[J]. Front Mech Eng, 2012, 7(2): 163-187.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-012-0324-5
https://academic.hep.com.cn/fme/EN/Y2012/V7/I2/163

Fig.1 Three manipulators and their coordinate systems. (a) CUH; (b) CRU; (c) CPU

Tab.1 Link parameters and variables of the CUH manipulator

Tab.2 Link parameters and variables of the CRU manipulator

Tab.3 Link parameters and variables of the CPU manipulator

Fig.2 Inverse singular configuration and suggestion—CUH

Fig.3 Five direct singular configurations for CUH—Case 1

Fig.4 Two direct singular configurations for CUH—Case 2

Fig.5 Two direct singular configurations for CUH—Case 3

Fig.6 Two direct singular configurations for CUH—Case 4

Fig.7 Three inverse singular configurations for CRU—Case 1

Fig.8 Three inverse singular configurations for CRU— Case 2

Fig.9 Two inverse singular configurations for CPU—Case 1

Fig.10 Two inverse singular configurations for CPU—Case 2

Tab.4 Given data for the CUH manipulator

Fig.11 Workspace of CUH in plane

Fig.12 Possible cross-section view of CUH workspace

Fig.13 Surfaces and contours of CUH workspace. (a) 3D graphic surfaces and contours of the highest and values; (b) 3D graphic surfaces and contours of the lowest and values

Tab.5 Given data for the CRU manipulator

Fig.14 Workspace of CRU in plane

Fig.15 Surfaces and contours of CRU workspace. (a) 3D graphic surfaces and contours of the highest and values; (b) 3D graphic surfaces and contours of the lowest and values

Fig.16 Singular configuration in CRU workspace

Tab.6 Given data for the CPU manipulator

Fig.17 Workspace of CPU in plane

Fig.18 Surfaces and contours of CPU workspace. (a) 3D graphic surfaces and contours of the highest and values; (b) 3D graphic surfaces and contours of the lowest and values

Fig.19 Condition number and its inverse with the fixed actuated translations—CUH

Fig.20 Condition number and its inverse with the fixed actuated rotations—CUH

Fig.21 Condition number and its inverse with one fixed actuated limb—CUH

Fig.22 Condition number and its inverse with the fixed actuated translations—CRU

Fig.23 Condition number and its inverse with the fixed actuated rotations—CRU

Fig.24 Condition number and its inverse with one fixed actuated limb—CRU

Fig.25 Condition number and its inverse with the fixed actuated translations—CPU

Fig.26 Condition number and its inverse with the fixed actuated rotations—CPU

Fig.27 Condition number and its inverse with one fixed actuated limb—CPU

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