This paper presents a closed-form formulation and geometrical interpretation of the derivatives of the Jacobian matrix of fully parallel robots with respect to the moving platforms’ position/orientation variables. Similar to the Jacobian matrix, these derivatives are proven to be also groups of lines that together with the lines of the instantaneous direct kinematics matrix govern the singularities of the active stiffness control. This geometric interpretation is utilized in an example of a planar 3 degrees-of-freedom redundant robot to determine its active stiffness control singularity.
Geometric Interpretation of the Derivatives of Parallel Robots’ Jacobian Matrix With Application to Stiffness Control
Contributed by the Mechanics and Robotics Committee for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received December 2000; revised February 2002. Associate Editor: S. K. Agrawal.
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Simaan, N., and Shoham, M. (March 21, 2003). "Geometric Interpretation of the Derivatives of Parallel Robots’ Jacobian Matrix With Application to Stiffness Control ." ASME. J. Mech. Des. March 2003; 125(1): 33–42. https://doi.org/10.1115/1.1539514
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