Positioning 3R manipulators may have two or four inverse kinematic solutions (IKS). This paper derives a necessary and sufficient condition for 3R positioning manipulators with orthogonal joint axes to have four distinct IKS. We show that the transition between manipulators with two and four IKS is defined by the set of manipulators with a quadruple root of their inverse kinematics. The resulting condition is explicit and states that the last link length of the manipulator must be greater than a quantity that depends on three of its remaining DH parameters. This result is of interest for the design of new manipulators.
A DH-Parameter Based Condition for 3R Orthogonal Manipulators to Have Four Distinct Inverse Kinematic Solutions
Contributed by the Mechanics and Robotics Committee for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received October 21, 2003; revised May 11, 2004. Associate Editor: C. Mavroidis.
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Wenger , P., Chablat , D., and Baili , M. (March 2, 2005). "A DH-Parameter Based Condition for 3R Orthogonal Manipulators to Have Four Distinct Inverse Kinematic Solutions ." ASME. J. Mech. Des. January 2005; 127(1): 150–155. https://doi.org/10.1115/1.1828460
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