Two optimization studies on the design of a three degree of freedom translational parallel platform are conducted and the results are compared. The objective function of the first study maximizes total volume of the manipulator workspace without regard to the quality of the workspace. The second study optimizes the total volume of well conditioned workspace by maximizing a global condition index. The global condition index is a function of the condition number of the Jacobian matrix, providing a means of measuring the amplification error between the actuators and the end effector. Both objective functions involve an integration over the workspace of the manipulator. This integral is approximated using the Monte Carlo method.

A novel 3-DOF parallel manipulator is presented that employs only revolute joints and constrains the manipulator output to translational motion. Closed-form solutions are developed for both the inverse and forward kinematics. The inverse kinematics produces four solutions for each leg of the manipulator. In general, the four solutions are realized in only two unique leg configurations. The forward kinematic solution is reduced to a quadratic equation. So that in general, there are two poses the manipulator can assume for a given set of input joint angles.

Provides algorithms for reorienting linked rigid bodies floating in space. The dynamics of these systems conserve both linear and angular momentum. The conservation of angular momentum is a nonintegrable or nonholonomic constraint. The authors derive this constraint by applying Noether's theorem to the Lagrangian of the system. When the total angular momentum is zero, the authors may dualize the constraint to a control system. The problem of reorienting the satellite becomes a steering problem for a drift free control system. The authors give explicit solutions for steering a planar skater and a satellite with two rotors. The planar skater has been simulated and animated on a graphics workstation. The authors also discuss the hardware setup which they built to verify the theoretical results.>

Methods for steering car-like robots with trailers are investigated. A connection is demonstrated between Murray and Sastry's (1990, 1991) work of steering with integrally related sinusoids and Sussmann and Liu's (1991) recent work on asymptotic behavior of systems with high-frequency sinusoids as inputs. The merits of coordinate transformations, relative to the convergence properties, are discussed. Simulation results for a car-like robot with two trailers are presented.>

A technique for stabilizing nonholonomic systems to trajectories is presented. It is well known that such systems cannot be stabilized to a point using smooth static-state feedback. The authors suggest the use of control laws for stabilizing a system about a trajectory, instead of a point. Given a nonlinear system and a desired nominal feasible trajectory, an explicit control law which will locally exponentially stabilize the system to the desired trajectory is given. The theory is applied to several examples, including a car-like robot.>