A direct kinematic computation algorithm for all planar 3-legged platforms /

An analysis and comprehensive solution to the direct kinematics problem (DK) of all planar 3-legged platforms with lower pairs, called general planar Stewart-Gough platform (PSGP), is presented. There are 10 types of PSGP DK problem formulation including those with mixed leg architecture.Planar kinematic mapping expresses pole position and rotation angle of a planar displacement as a point in 3-dimensional projective space represented by 4 homogeneous coordinates. This provides a universal tool for kinematic analysis. Its application will be demonstrated in the derivation of a general algorithm for planar DK. For each type of PSGP, the problem is reduced to a 6th order univariate polynomial whose roots reveal all solutions. An example of a PSGP with 6 real assembly configurations is presented. Furthermore, this algorithm was implemented and tested exhaustively. A complete self-contained version, coded in C, is available at http://www.cim.mcgill.ca/∼paul/. It should be easy to customize and adapt to any given real time micro-controller application