Analytical Solution of the Forward Displacement Problem for Spherical   Parallel Manipulators
  In this paper, an analytical method that solves the forward displacement problem of several common spherical parallel manipulators (SPMs) is presented. The method uses the the quaternion algebra to restate the problem as a system of four quadrics in four variables and uses an algebraic geometry result by Dixon from 1908 to solve. In addition, a case study is presented for a specific SPM. 
Jose Rodriguez, Maurizio Ruggiu
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