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Research Papers

Formulation of Unique Form of Screw Based Jacobian for Lower Mobility Parallel Manipulators

[+] Author and Article Information
Man Bok Hong1

Department of Mechanical Engineering, Yonsei University, 134 Sinchon-dong, Seodaemun-gu, Seoul 120-749, Koreamanbok.hong@gmail.com

Yong Je Choi

Department of Mechanical Engineering, Yonsei University, 262 Seongsanno, Seodaemun-gu, Seoul 120-749, Koreayjchoi@yonsei.ac.kr

1

Present address: Biomedical Engineering Branch, Division of Convergence Technology, National Cancer Center, 323 Ilsan-ro, Ilsandong-gu, Goyang-si, Gyeonggi-do 410-769, Korea.

J. Mechanisms Robotics 3(1), 011002 (Nov 23, 2010) (6 pages) doi:10.1115/1.4002696 History: Received January 31, 2010; Revised September 15, 2010; Published November 23, 2010; Online November 23, 2010

In this paper, the unique form of the screw based Jacobian is suggested for lower mobility parallel manipulators. Utilizing the concept of the reciprocal Jacobian, the forward statics relation for each of the serial kinematic chains of a parallel manipulator can be first obtained and then used to derive both the forward statics and the inverse velocity relations of the manipulator. The screw based Jacobian of a parallel manipulator can be formulated from the inverse velocity relation in such a way that it consists of the reciprocal Jacobians of the serial kinematic chains. Since any reciprocal Jacobian is unique to the corresponding serial chain, the suggested form of the screw based Jacobian is also determined uniquely to the lower mobility parallel manipulator. Two examples are given to illustrate the proposed method, one for the 3DOF parallel manipulator with three identical prismatic-revolute-spherical joints-serial chains and the other for the 4DOF parallel manipulator with nonidentical serial chains (two spherical-prismatic-spherical- and one revolute-revolute-prismatic-revolute joints-serial chains).

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Figures

Grahic Jump Location
Figure 1

Joint screws of an n-DOF serial chain

Grahic Jump Location
Figure 2

3DOF parallel manipulator with three PRS-serial chains. (a) Schematic of the manipulator. The row screws of Jacobian, ûis of the parallel manipulator, are marked with white arrowheads. (b) Column screws of the Jacobian, Ŝjs (black arrowheads), of the ith PRS-serial chain.

Grahic Jump Location
Figure 3

Column screws of the reciprocal Jacobian, ŝr,js (with white arrowheads), of the ith PRS-serial chain

Grahic Jump Location
Figure 4

4-DOF parallel manipulator with two SPS- and one RRPR-serial chains. (a) Schematic of the manipulator. The row screws of the Jacobian of the parallel manipulator are marked with white arrowheads. (b) Column screws of the Jacobian, Ŝjs (black arrowheads), of the RRPR-serial chain.

Grahic Jump Location
Figure 5

Column screws of the reciprocal Jacobian, ŝr,js (white arrowheads), of the RRPR-serial chain.

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