Introducing differential kinematics to mechanical engineering students

Differential kinematics offers a simplified alternative to closed-form input-output equations needed to study the geometrical behaviour of linkages. For most linkages, these closed-form equations are either too messy or not possible to obtain, a fact that sometimes reflects negatively on how mechanical engineering students perceive the subject of mechanism analysis. On the other hand, differential models can easily be utilised in numerical methods designed to encourage these students to tackle even more difficult problems than currently being considered in academic programmes. In this paper, an approach is presented to facilitate this process. The mathematical procedure is based on the use of matrices referred to as kinematic Jacobians. The determinants of these matrices offer invaluable insights into the linkage mobility. These matrices are explained and used in a practice numerical example.