A method for transient dynamic analysis of planar mechanisms consisting of constrained rigid and flexible bodies is developed, accounting for coupled large displacements and small elastic deformation.
For each flexible body, two sets of generalized coordinates are employed. First, reference generalized coordinates define the location of a body fixed coordinate system with respect to the inertial reference frame. Second, the generalized coordinates corresponding to elastic deformation are introduced through the modal analysis technique using the finite element method. The main advantage of using modal coordinates is the reduction in number of coordinates that must be determined in the analysis.
For modal analysis, lumped mass approach and cubic polynomial shape functions are used to characterize deformation of mechanical systems, allowing both longitudinal and transverse deformations.
The system equations of motion are formulated using Lagrange's equations and the system equations of motion and constraints equations are combined through a Lagrange multiplier technique.
The equations of motion and constraints are solved numerically using a direct integration method and generalized coordinate partitioning method. This generalized coordinate partitioning is employed to reduce the number of degree of freedom, and increase the efficiency of the computer program.
The results obtained by the presented method and those available in the literature are in the good agreement.