Many numerical integrators for mechanical system simulation are created by using discrete algorithms to approximate the continuous equations of motion. In this paper, we present a procedure to construct time-stepping algorithms that approximate the flow of continuous ODE'S for mechanical systems by discretizing Hamilton's principle rather than the equations of motion. The discrete equations share similarities to the continuous equations by preserving invariants, including the symplectic form and the momentum map. We first present a formulation of discrete mechanics along with a discrete variational principle. We then show that the resulting equations of motion preserve the symplectic form and that this formulation of mechanics leads to conservation laws from a discrete version of Noether's theorem. We then use the discrete mechanics formulation to develop a procedure for constructing mechanical integrators for continuous Lagrangian systems. We apply the construction procedure to the rigid body and the double spherical pendulum to demonstrate numerical properties of the integrators.

This paper studies variational principles for mechanical systems with symmetry and their applications to integration algorithms. We recall some general features of how to reduce variational principles in the presence of a symmetry group along with general features of integration algorithms for mechanical systems. Then we describe some integration algorithms based directly on variational principles using a discretization technique of Veselov.The general idea for these variational integrators is to directly discretize Hamilton's principle rather than the equations of motion in a way that preserves the original systems invariants, notably the symplectic form and, via a discrete version of Noether's theorem, the momentum map. The resulting mechanical integrators are second-order accurate, implicit, symplectic-momentum algorithms. We apply these integrators to the rigid body and the double spherical pendulum to show that the techniques are competitive with existing integrators.

Minimally invasive surgical techniques, especially endoscopy and laparoscopy, possess many advantages over conventional methods. These include accelerated patient recovery and reduced rate of complications. However, limitations of current operating instruments create difficulties for the surgeon. In this article, we present a design for an improved polypectomy snare for the endoscope, several rotary actuator designs for endoscopic tools, and a prototype endo‐platform, which provides fine motion control for endoscopic tools. We also present several prototypes of more dextrous laparo‐scopic tools based on the human hand. Finally, we present a sensory glove designed as a natural and dextrous human interface. © 2995 John Wiley & Sons, Inc.