the primary mathematical tool for the analysis of a linkage is known as the kinematics equations of the system. this is a sequence of rigid body transformation along a serial chain within the linkage that locates a floating link relative to the ground frame. each serial chain within the linkage that connects this floating link to ground provides a set of equations that must be satisfied by the configuration parameters of the system. the result is a set of non-linear equations that define the configuration parameters of the system for a set of values for the input parameters.