ABSTRACT
This chapter discusses the method of joint-coordinate formulation that has most of the advantages of both the body-coordinate and vectorial formulations. It discusses two composite joints: revolute–revolute and revolute–translational. The main purpose for introducing these joints in the body-coordinate formulation was to reduce the number of coordinates and constraints in a model. The joint-coordinate method provides a systematic process that transforms the large set of equations of motion from the body-coordinate formulation to a smaller or possibly a minimal set of equations. The chapter follows the traditional vector-loop method to construct the cut-joint arrays and matrices that are needed for the equations of motion. A joint coordinate, as its name suggests, describes the degree of freedom (DoF) that a joint allows between two bodies. The chapter derives recursive formulas to compute the coordinates and velocity of body, assuming that the coordinates and velocity of body and those for joint are known.
