Dynamic Response Analysis of Complex Mechanisms with Multiple Inputs

Download or read book Dynamic Response Analysis of Complex Mechanisms with Multiple Inputs written by Charles Edward Benedict and published by . This book was released on 1971 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: The holonomic constraints associated with complex, multiple input linkage systems complicate the procedures and methods used in determining their dynamic response. Large systems of nonlinear, second-order differential equations, requiring additional algebraic equations of constraint, occur as a result of these constraints. Double iteration algorithms, which are both time-consuming and subject to error, are necessary to integrate numerically these differential equations of motion. In this dissertation the concepts of kinematic influence coefficients of complex, planar, rigid link mechanisms with multiple inputs are developed and utilized to eliminate the holonomic constraints associated with such systems. Kinematic influence coefficients associated with series and parallel linkage combinations are developed, based on the addition of Assur groups (dyads, tetrads and more complex groups) to the basic system group. These complex, multiple input linkage systems are then reduced to coupled equivalent mass systems acted upon by variable rate springs, variable coefficient viscous dampers, and equivalent external forces and torques. The holonomic constraints associated with the original system are eliminated, thus leaving the equivalent mass system free of all such constraints. The number of generalized coordinates required to describe the motion of the equivalent system now equals the number of independent system inputs. The differential equations of motion describing the system's dynamical behavior can then be determined by established methods and put in a suitable form for numerical integration.