Displacement Analysis of Two Special Cases of the TTTR Mechanisms

A pair of quartic polynomials in the tangent of the output angular displacement were derived for two TTTR mechanisms designed in such a way that the serially connected pairs of Hooke joints have their successive transverse axes parallel or mutually perpendicular. These results form the basis for an efficient reverse displacement analysis and for the design of a new group of robots with three serially connected Hooke joints which may prove to be attractive to industry.