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Kinematic analysis of the 3-RPS-3-SPR series–parallel manipulator
Abhilash Nayak, Stéphane Caro, Philippe Wenger
Journal:

Robotica / Volume 37 / Issue 7 / July 2019

Published online by Cambridge University Press:

24 August 2018, pp. 1240-1266
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This paper deals with the kinematic analysis and enumeration of singularities of the six degree-of-freedom 3-RPS-3-SPR series–parallel manipulator (S–PM). The characteristic tetrahedron of the S–PM is established, whose degeneracy is bijectively mapped to the serial singularities of the S–PM. Study parametrization is used to determine six independent parameters that characterize the S–PM and the direct kinematics problem is solved by mapping the transformation matrix between the base and the end-effector to a point in ℙ7. The inverse kinematics problem of the 3-RPS-3-SPR S–PM amounts to find the location of three points on three lines. This problem leads to a minimal octic univariate polynomial with four quadratic factors.