Computer aided motion synthesis for improved kinematic and dynamic performance of mechanical systems

This thesis deals with the problem of computer aided motion synthesis for computer controlled machinery. The first part of the thesis studies the problem of motion synthesis in the cartesian space and presents methods for synthesizing and fine-tuning spatial motions with desired kinematic performance. A dual-quaternion representation of spatial displacements is adopted and the problem of cartesian motion synthesis is studied as a curve design problem in the space of dual quaternions. The results include a measure for global smoothness of a cartesian motion, a spherical algorithm for synthesizing parametrically continuous and globally smooth cartesian motions, as well as two algorithms for fine-tuning the path and speed of rational B-spline cartesian motions. The path-smoothing algorithm automatically detects and smoothes out the third order geometric discontinuities in the path of a rational B-spline motion defined by a cubic B-spline dual quaternion curve. The speed-smoothing algorithm uses a quintic rational B-spline dual quaternion curve to obtain a second-order geometric approximation of the path of a cubic rational B-spline dual quaterion curve while allowing specification of the speed and the rate of change of speed at the key points to obtain a near constant kinetic energy parameterization. The notion of kinetic energy is used as a natural way of combining the rotational and translational speed of a spatial motion. These results have applications not only in cartesian motion planning of computer controlled machinery but also in camera motion planning and spatial navigation in visualization and virtual reality systems as well as in mechanical system simulation.; The second part of thesis presents methods for synthesizing low-harmonic Bezier and B-spline joint trajectories for high-speed and high-accuracy computer controlled machinery where vibration reduction is a major concern. These trajectories have the advantage that not only they are compatible with the existing NURBS based CAD system but their harmonic content can be tailored to avoid excitation of the natural modes of vibration of the system as well. These low-harmonic curves are used for constructing high-speed cam profiles, for approximating cubic Bezier and B-spline curves to filter out higher harmonic components, as well as for trajectory generation of computer controlled machinery.