| This thesis addresses several aspects of the dynamics and control of mechanical systems, particularly those which contain closed kinematic chains. When a mechanical system contains closed chains, many aspects of its kinematics, dynamics, and control become more complicated. The generalized coordinates describing the configuration of the system must have values which satisfy a set of nonlinear configuration constraint equations; the generalized speeds describing the motion of the system must have values which satisfy a set of linear motion constraint equations; and the formulation of the system's dynamical equations must account for the fact that the generalized speeds are no longer independent of each other.; To aid in the determination of generalized coordinate values which are consistent with configuration constraints, improvements to the Kane-Davidenko and Newton-Raphson methods for solving sets of nonlinear equations are developed. Since both these methods require forming the partial derivatives of the nonlinear expressions, a procedure is presented for determining the partial derivatives of configuration constraint expressions without performing either symbolic or numeric differentiation. A method is set forth which automates the selection of independent generalized speeds, facilitating the use of the embedded constraint handling, which produces efficient dynamical equations for systems with motion constraints. Procedures are presented for forming simplified second-order dynamical equations for both open-chain and closed-chain systems. These dynamical equations can be used to reduce the number of calculations required to implement Computed Torque control.; A particular type of closed-chain system is the Stewart Platform, a six-degree-of-freedom parallel mechanism consisting of a platform connected to a base by six linear actuator legs. Previously, the dynamical equations for the Stewart Platform have only been formed when the inertia of the legs is neglected or approximated. The formulation of the dynamical equations of the Stewart Platform is presented, accounting for the full effects of the leg inertia. One of the disadvantages of the Stewart Platform is the presence of singular positions, where the actuators are positioned such they cannot produce arbitrary acceleration. A variation of the Stewart Platform, called the Redundant-Leg Stewart Platform, is proposed, which possesses more than the conventional six actuators. These additional legs complicate the analysis but improve the controllability of the mechanism, lowering the required control forces and eliminating singular positions. |
