PLEXUS — Software for the Numerical Analysis of the Dynamical Behavior of Rigid and Flexible Mechanisms

In most computer codes developed for the dynamic analysis of mechanisms, such as the serial manipulators used in Robotics, differential equations of motion are derived from the hypothesis that the links are rigid while flexibilities, if any, are located at the joints. This simplification is widely used since it correctly models the sturdy members found in present robots while limiting the number of unknown parameters and of the related kinematical and dynamical equations. Indeed, a rigid body shows six degrees of freedom, and any connection between two adjacent members removes up to five possibilities of relative motion: the total number of independent position parameters of any complex mechanism remains small, and elaborating the kinematical models for the end effector is then a straightforward procedure (the geometrical model relates its position and orientation to the joint parameters, while the differential model expresses its linear and angular velocities in terms of the time derivatives of joint parameters), [1].