Model equations of planar and spatial joints

Abstract

Joints prevent a body from either moving along one or several axes, or from rotating around one or several axes, or both. As a consequence, joints reduce the number of DOFs of a body or of a mechanism and thereby constrain their motion. Therefore mathematical models of joints are called constraint equations (constraint position, velocity, or acceleration equations). Theoretical models of joints (between a body and the ground) that constrain the motion of a body with respect to the ground are called absolute constraint equations, whereas models of joints (between two bodies) that constrain the relative motion of two bodies, are called relative constraint equations.