One of the most important and widely used concepts in the kinematic analysis of robot manipulators is the reciprocal screw. However, there are no general expressions and easy methods to obtain the reciprocal screw in an analytic manner. This paper suggests an analytic formulation of the reciprocal screws of arbitrarily aligned screw systems. Since the reciprocal screws obtained in this paper are represented by the direction vectors and the position vectors of the given screws, we can analyze the relation between the reciprocal screw system and the given screw system easily. With the results, to find a reciprocal screw is to solve an algebraic equation of the corresponding system of screws. In order to show the usefulness of the result, several examples related to the robot manipulator are provided. For a nonredundant serial manipulator, the pseudo inverse of the Jacobian matrix is shown to be equivalent to the wrench matrix obtained by the reciprocity. For a parallel manipulator, a leg is isolated to obtain an independent part from the manipulator and is analyzed analytically. The proposed method can be applied to any arbitrarily aligned screw system.
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March 2003
Technical Papers
Analytic Formulation of Reciprocal Screws and Its Application to Nonredundant Robot Manipulators
Wan Kyun Chung, Professor
e-mail: wkchung@postech.ac.kr
Wan Kyun Chung, Professor
Robotics & Bio-Mechatronics Lab., Department of Mechanical Engineering, POSTECH(Pohang University of Science & Technology) Nam-Gu Hyoja-Dong San 31, Pohang, KyongBuk, 790-784, South Korea
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Wan Kyun Chung, Professor
Robotics & Bio-Mechatronics Lab., Department of Mechanical Engineering, POSTECH(Pohang University of Science & Technology) Nam-Gu Hyoja-Dong San 31, Pohang, KyongBuk, 790-784, South Korea
e-mail: wkchung@postech.ac.kr
Contributed by the Mechanics and Robotics Committee for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received June 2001. Associate Editor: M. Raghavan.
J. Mech. Des. Mar 2003, 125(1): 158-164 (7 pages)
Published Online: March 21, 2003
Article history
Received:
June 1, 2001
Online:
March 21, 2003
Citation
Kim, D., and Chung, W. K. (March 21, 2003). "Analytic Formulation of Reciprocal Screws and Its Application to Nonredundant Robot Manipulators ." ASME. J. Mech. Des. March 2003; 125(1): 158–164. https://doi.org/10.1115/1.1539508
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