In this paper, the geometric design problem of serial-link robot manipulators with three revolute (R) joints is solved using a polynomial homotopy continuation method. Three spatial positions and orientations are defined and the dimensions of the geometric parameters of the 3-R manipulator are computed so that the manipulator will be able to place its end-effector at these three pre-specified locations. Denavit and Hartenberg parameters and 4×4 homogeneous matrices are used to formulate the problem and obtain eighteen design equations in twenty-four design unknowns. Six of the design parameters are set as free choices and their values are selected arbitrarily. Two different cases for selecting the free choices are considered and their design equations are solved using polynomial homotopy continuation. In both cases for free choice selection, eight distinct manipulators are found that will be able to place their end-effector at the three specified spatial positions and orientations.
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December 2002
Technical Papers
Solving the Geometric Design Problem of Spatial 3R Robot Manipulators Using Polynomial Homotopy Continuation
Eric Lee, Graduate Student, Student Mem. ASME,
Eric Lee, Graduate Student, Student Mem. ASME
Robotics and Mechatronics Laboratory, Department of Mechanical and Aerospace Engineering, Rutgers University, The State University of New Jersey, 98 Brett Rd., Piscataway, NJ 08854
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Constantinos Mavroidis, Associate Professor, Mem. ASME
Constantinos Mavroidis, Associate Professor, Mem. ASME
Robotics and Mechatronics Laboratory, Department of Mechanical and Aerospace Engineering, Rutgers University, The State University of New Jersey, 98 Brett Rd., Piscataway, NJ 08854
Search for other works by this author on:
Eric Lee, Graduate Student, Student Mem. ASME
Robotics and Mechatronics Laboratory, Department of Mechanical and Aerospace Engineering, Rutgers University, The State University of New Jersey, 98 Brett Rd., Piscataway, NJ 08854
Constantinos Mavroidis, Associate Professor, Mem. ASME
Robotics and Mechatronics Laboratory, Department of Mechanical and Aerospace Engineering, Rutgers University, The State University of New Jersey, 98 Brett Rd., Piscataway, NJ 08854
Contributed by the Mechanisms and Robotics Committee for publication in the Journal of Mechanical Design. Manuscript received March 2001. Associate Editor: G. S. Chirikjian.
J. Mech. Des. Dec 2002, 124(4): 652-661 (10 pages)
Published Online: November 26, 2002
Article history
Received:
March 1, 2001
Online:
November 26, 2002
Citation
Lee, E., and Mavroidis, C. (November 26, 2002). "Solving the Geometric Design Problem of Spatial 3R Robot Manipulators Using Polynomial Homotopy Continuation ." ASME. J. Mech. Des. December 2002; 124(4): 652–661. https://doi.org/10.1115/1.1515796
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