Dynamics of an elastic multibody chain: Part D—Modelling of joints

Abstract

In the three previous papers in this series on the dynamics of a topological chain of arbitrary elastic bodies, rotational and translational displacements of arbitrary magnitude were allowed at all interbody joints. While this degree of generahty lends relevance withrespect to a diverse range of robotics applications, a careful specification of the displacement and force components at each joint becomes mandatory. In the present analysis, from one to six degrees of freedom are permitted at each joint, as reflected in the number of columns in its joint projection matrix. The special but practically important cases ofrotational (revolute) joints with one, two or three degrees of freedom are considered in detail, including physical interpretations for the coefficient matrices in the equations of motion. With robotics applications in mind, the many possibilities for sensors and actuators at the joints are catalogued and the four most important classes of ‘sensactor’ (a colocated sensor/actuator pair) are identified and their implications for the system equations presented.