THE MECHANICS OF PARALLEL MECHANISMS AND WALKING MACHINES

A parallel mechanism is one whose links and joints form two or more se rially connected chains which join the fixed base and the end effector . The mechanism of a multi-legged walking machine can be considered as a parallel mechanism whose base is not fixed and whose configuration changes during different phases of its gait. This paper presents metho ds for analysing the mechanics of parallel mechanisms and walking mach ines using vector and screw algebra. Firstly, displacement analysis is covered; this includes general methods for deriving the position vect or of any joint in any leg and for calculating the active joint displa cements in any leg. Secondly, velocity analysis is covered which tackl es the problem of calculating active joint velocities given the veloci ty, position and the orientation of the body and the positions of the feet. Thirdly, the static analysis of these classes of mechanisms usin g the principle of virtual work and screw algebra is given. Expression s are derived for the actuator forces and torques required to balance a given end effector (or body) wrench and, in the case of a walking ma chine, the ground reactions at the feet. Numerical examples are given to demonstrate the application of these methods.