Incremental kinematic analysis and symbolic synthesis of mechanisms

Kinematic design is an important aspect of the design of mechanical systems with moving parts. The performance of such systems may suffer from the presence of parts that get stuck during their motion causing jams, or that execute undesired motions. Kinematic analysis needs to be conducted and the design of the system modified. Analysis-redesign-reanalysis cycles are common in reaching a satisfactory design. If the system is large and the incidence of redesign frequent, then the speed of computation during the re-analysis cycle becomes a concern. Faster re-analysis methods are needed. This work addresses this problem by providing computational techniques for doing incremental kinematic analysis. The mechanism is represented as a graph of objects with connection constraints among them. A recursive procedure traverses the graph to establish instantaneous kinematic properties. A store-and-reuse strategy is employed to increase the efficiency of re-analysis runs. This involves storing intermediate results of computations for reuse in case of incremental redesign or iterative analysis. A comparative, quantitative study of the normal, "from-scratch" method and the incremental method is provided to prove the greater efficiency of the latter.;The other topic dealt with in this work is kinematic synthesis. Methods of obtaining serial chains of specified twistspace are proposed. Procedures are also developed that, for mechanisms which prove to be defective, can determine appropriate solutions to rectify the problem. Given the nature of the problems in kinematic design, their solutions typically entail relieving overconstrained parts of some of their constraints or constraining the undesired degrees of freedom of underconstrained parts. The procedures determine various alternatives for achieving the desired kinematic goal. Number- and type-synthesis are the specific concerns, and are addressed by a generate-and-test approach. Also of interest are the special geometric configurations of the mechanism in which it gains or loses degrees of freedom. The procedures return information in symbolic form. This is useful to the designer because it lets him work with ranges of values and relations between the geometric parameters of the systems rather than having to commit to one numeric design. The representation of, and reasoning about, motions and forces is based on the principles of screw theory.