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TECHNICAL PAPERS

Design and Control of a Compliant Parallel Manipulator

[+] Author and Article Information
Thomas G. Sugar

Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ 85287email: thomas.sugar@asu.edu

Vijay Kumar

General Robotics and Active Sensory, Perception, (GRASP) Laboratory, University of Pennsylvania, Philadelphia, PA 19104

J. Mech. Des 124(4), 676-683 (Nov 26, 2002) (8 pages) doi:10.1115/1.1517568 History: Received January 01, 2000; Online November 26, 2002
Copyright © 2002 by ASME
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References

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Kazerooni,  H., Sheridan,  T. B., and Houpt,  P. K., 1986, “Robust Compliant Motion for Manipulators, Part 1: The Fundamental Concepts of Compliant Motion,” IEEE J. Rob. Autom., RA-2(2), pp. 83–92.
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Figures

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The three degree-of-freedom, in-parallel, actively controlled arm applies a force in the X and Y directions as well as a moment in the Z direction. Each limb has a spring attached in series to a linear actuator driven by a DC motor attached to a ball screw transmission.
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A schematic of the parallel manipulator
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The spring system for one limb
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General planar parallel mechanism
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The planar parallel manipulator
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Force deflection curves for the adjustable spring system
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Different transfer functions for the stiffness control of one link as Kdes is varied from 1.75 to 26.27 N/cm and Kact equals 17.51 N/cm. The transfer function compares the spring force to the link defection, fspring(s)/l(s).
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Different transfer functions for the stiffness control of one link as Kdes is varied from 1.75 to 26.27 N/cm and Kact equals 17.51 N/cm. The transfer function compares the total force to the link defection, ftot(s)/l(s). At high frequencies, the mass m1 dominates the response.
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Stiffness in the normal direction, desired (dashed) and actual. The normal force when Kyy=21.04 N/cm is shown on the right.
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Stiffness in the tangential direction, desired (dashed) and actual. The tangential force when Kxx=7.00 N/cm is shown on the right.
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Angular stiffness, desired (dashed) and actual. The moment when Kθθ=27110 Ncm/rad is shown on the right.
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Candidate designs. The design on the right possesses optimal transmission characteristics but is too bulky while the design on the left is the compromise design.
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Optimal planar parallel mechanism with constraints on the internal angles θ12, and θ3

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