• CN: 11-2187/TH
  • ISSN: 0577-6686

›› 2009, Vol. 45 ›› Issue (4): 50-55.

• Article • Previous Articles     Next Articles

Jacobian Analysis of Symmetrical 4-DOF 3R1T Parallel Mechanisms

LI Qinchuan;HU Xudong;CHEN Qiaohong;WU Chuanyu   

  1. Provincial Key Laboratory of Modern Textile Machinery, Zhejiang Sci-Tech University
  • Published:2009-04-15

Abstract: A method for Jacobian analysis of 4-DOF 3R1T parallel mechanism is proposed. The mobility analysis of 3R1T parallel mechanisms is performed by using displacement group theory. The motion of the moving platform of a 3R1T parallel mechanism is a four dimensional displacement manifold. Then, the Jacobian matrix of single limb kinematic chain is based on the basis of screw theory, which is a 6×5 non-square matrix. On the basis of the mobility property, it can be proven that the fourth and the fifth rows of the limb Jacobian matrix are redundant. Deleting the fourth row or the fifth row of the limb Jacobian matrix leads to a 5×5 matrix, which is of full rank in non-singular configurations. After the actuation of the 3R1T parallel mechanism is determined, the inverse of the 5×5 matrix of each limb can be obtained. A 4×5 non-square matrix can be obtained by combining the four row vectors corresponding to the actuated pairs taken from the four inverses. The elements of the fourth column of the 4×5 non-square matrix are always multiplied by 0 and thus are redundant. Deleting the fourth column of the 4×5 non-square matrix yields a 4×4 invertible matrix, the inverse of which is the Jacobian matrix of the 4-DOF 3R1T parallel mechanism. This method is straightforward and can be further applied in performance analysis and kinematic design of the 3R1T parallel mechanism.

Key words: Displacement group theory, Jacobian matrix, Parallel mechanism, Screw theory

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