A general, robust procedure for the kinematic and friction force analysis of single loop, one degree-of-freedom spatial mechanisms

The concepts presented in this dissertation represent a generalized method for the kinematic and friction force analysis of closed single loop, one degree-of-freedom mechanisms using transformation matrix techniques. The technique is very "building block" oriented and amenable to a computer programmable algorithm. A robust means for solving under and overconstrained systems of kinematic equations has been outlined using singular value decomposition. Initial closure of the mechanism loop is done using optimization techniques. Subsequent positions are solved using Newton's method and singular value decomposition. This approach is very useful for mechanisms possessing idle degrees-of-freedom or dead center positions. It also allows "special mobility" mechanisms such as planar mechanisms or maverick mechanisms (like the Bennett mechanism) to be analyzed as general spatial mechanisms. The friction problem is considered using Coulomb friction.;A general, three-dimensional surface contact joint based on transformation matrix techniques was also developed. This is a five degree-of-freedom joint. Both the kinematic and friction force characteristics of this joint have been presented. This joint may be used to model convex surfaces that contact at a single point. The surfaces are described parametrically. Either analytical definitions or piecewise continuous surface patches may be used to describe the contacting surfaces.;Additionally, a friction model for the lower pair spherical joint was developed. This allows the friction characteristics of a spherical joint to be accurately considered. Lower pair equivalents for the spherical joint do not exhibit the same joint bearing forces as the actual "ball and socket" in a spherical joint. This model assumes the spherical joint behaves instantaneously as a revolute joint with an axis along the instant screw axis between the two links joined by the spherical joint. The effective pin radius is a function of the joint bearing forces and the coefficient of friction.