Rigid-body motions

Abstract

Mechanism is made up of links and kinematic pair joints which move in the three-dimensional space. Many physical objects are considered as rigid bodies for the convenience of theoretical analysis. For rigid body motions, the representations of rigid body rotation have a wide range of approaches including the representations from the directional cosine matrix to the exponential coordinates. The kinematics of rigid body is the motion analysis without considering any external forces acting on a rigid body, which is actually the foundation of the dynamics of rigid bodies. This chapter firstly presents the representation method of the position and orientation of rigid bodies using both the algebraic and the geometric methods. Then, an example of a SCARA robot is given to show the applications of the basic theoretical tools for rigid body motions. The purpose of this chapter is to provide the basic mathematical tools and the main results for the kinematics of rigid body though many objects may have elastic deformation in practical engineering problems.