A New Polynomial Solution to the Geometric Design Problem of Spatial R-R Robot Manipulators Using the Denavit and Hartenberg Parameters
Author:
Mavroidis Constantinos1, Lee Eric1, Alam Munshi1
Affiliation:
1. Robotics and Mechatronics Laboratory, Department of Mechanical and Aerospace Engineering, Rutgers University, The State University of New Jersey, 98 Brett Rd., Piscataway, NJ 08854
Abstract
This paper presents a new method to solve the geometric design problem of spatial two degrees of freedom, open loop robot manipulators with revolute joints that perform tasks, which require the positioning of the end-effector in three spatial locations. Tsai and Roth [3] solved this problem first using screw parameters to describe the kinematic topology of the R-R manipulator and screw displacements to obtain the design equations. The new method, which is developed in this paper, uses Denavit and Hartenberg parameters and 4×4 homogeneous matrices to formulate and obtain the kinematic equations. The loop-closure geometric equations provide eighteen design equations in eighteen unknowns. Polynomial Elimination techniques are used to solve these equations and obtain the manipulator Denavit and Hartenberg parameters and the manipulator base and end-effector geometric parameters. A sixth order polynomial is obtained in one of the design parameters. Only two of the six roots of the polynomial are real and they correspond to two different robot manipulators that can reach the desired end-effector poses.
Publisher
ASME International
Subject
Computer Graphics and Computer-Aided Design,Computer Science Applications,Mechanical Engineering,Mechanics of Materials
Reference38 articles.
1. Kota, S., and Erdman, A., 1997, “Motion Control in Product Design,” Mech. Eng. (Am. Soc. Mech. Eng.), 119, No. 8, pp. 74–77. 2. McCarthy, M. J., 2000, “Mechanisms Synthesis Theory and the Design of Robots,” Proceedings of the 2000 IEEE International Conference on Robotics and Automation, April 24–28 2000, San Francisco, CA. 3. Tsai, L., and Roth, B., 1973, “A Note on the Design of Revolute-Revolute Cranks,” Mech. Mach. Theory, 8, pp. 23–31. 4. Suh, C. H. , 1969, “On the Duality of the Existence of R-R Links for Three Positions,” ASME J. Eng. Ind., 91B, No. 1, pp. 129–134. 5. Roth, B. , 1967, “Finite Position Theory Applied to Mechanism Theory,” ASME J. Appl. Mech., 34E, pp. 599–605.
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