Optimal synthesis of adjustable mechanisms for generating multiple continuous paths.

Flexibility is an essential aspect of today's manufacturing systems, provided chiefly by employing robots to replace classical hard automation. In many cases, however, flexibility needs are modest and can be met by adjustable mechanisms that retain important advantages of mechanism-based automation, such as accurate motion at high speed and low cost. This dissertation presents a general methodology for dimensional synthesis of adjustable mechanisms capable of tracing a set of pre-defined continuous paths by the adjustment of a few links of the mechanism. Potential applications for such mechanisms include welding, sealant application, fabric cutting, etc. A new formulation is presented for synthesis of mechanisms that generate a single path. Optimal synthesis is first performed for curve shape without regard to curve size, orientation or location. Curve shape is characterized using Fourier descriptors of the curve, commonly used in the pattern recognition field. This allows the optimization algorithm to search only the subspace of variables defining the shape of a coupler curve rather than the full design space. The solution mechanism is then scaled, translated and rotated using a procedure that minimizes the distance between a few specified points on the desired curve and their shape-wise analogous points on the generated curve. A three-step methodology is presented to extend the synthesis process to adjustable mechanisms as follows: (1) several mechanisms are synthesized that will generate the shape of the first desired curve with acceptable accuracy; (2) for each mechanism synthesized in (1), links are adjusted to generate the shapes of the other desired curves; (3) curves with nearly correct relative size, location and orientation are optimized. A two-stage global optimization algorithm is used: A simulated annealing algorithm for constrained optimization in continuous spaces performs a global search from a random point. This is followed by local optimization using Powell's method of conjugate directions. Results of this methodology applied to several example problems are very encouraging. Paths of practical significance can be generated without requiring user intervention.PhDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/104401/1/9513497.pdfDescription of 9513497.pdf : Restricted to UM users only