Recent results have shown that the application of group theory to the Euclidean group, E(3), and its subgroups yields a new and improved mobility criterion. Unlike the well known Kutzbach-Gru¨bler criterion, this improved mobility criterion yields correct results for both trivial and exceptional linkages. Unfortunately, this improved mobility criterion requires a little bit more than counting links and kinematic pairs. An important advance was made when it was proved that the improved mobility criterion, originally stated in a language of group theory and subsets and subgroups of the Euclidean group, E(3), can be translated into a language of the Lie algebra, e(3), of the Euclidean group, E(3), and its vector subspaces and its subalgebras. The language of the Lie algebra, e(3), is far simpler than the nonlinear language of the Euclidean group, E(3). Still, the computations required for the improved mobility criterion are more involved than those required for the Kutzbach-Gru¨bler criterion, and it might preclude the employment of the improved mobility criterion in prospective tasks such as the number synthesis of parallel and modular manipulators. This contribution dispels these doubts by showing that the improved criterion can be easily implemented by a simple computer program. Several examples are included.
A simple computer program for calculating PSA recurrence in prostate cancer patients
