The Incorporation of Arc Boundaries and Stick/Slip Friction in a Rule-Based Simulation Algorithm for Dynamic Mechanical Systems with Changing Topologies

Abstract

Many dynamic mechanical systems, such as parts-feeders and percussive power tools, are described by equations of motion which are discontinuous. The discontinuities result from kinematic constraint changes which are difficult to foresee, especially in presence of impact and friction. A simulation algorithm for these types of systems must be able to algorithmically predict and detect the kinematic constraint changes without any prior knowledge of the system’s motion. This paper presents a rule-based approach to the prediction and detection of kinematic constraint changes between bodies with arc and line boundaries. A new type of constraint change, constraint exchange, is characterized. When arc contact exists, stick/slip friction is the difference between pure rolling and rolling with slip. Therefore, stick/slip friction is included in the algorithm. A force constraint is applied to the equations of motion when additional kinematic constraints due to friction would render the coefficient matrix singular. The efficacy of the rule-based simulation algorithm as a design tool is demonstrated through the design and experimental validation of a parts-feeder. The parts-feeder design is validated through two means: (1) a frame-by frame comparison of simulation results with the part motion recorded by high speed video and (2) actual testing.