TABLE OF CONTENTS The planar slider crank mechanism shown in Fig. 7 consists of four bodies: the fixed link (ground), denoted as body 1, the crankshaft OA (body 2), the connecting rod AB (body 3), and the slider block (body 4) at B. All bodies are assumed to be rigid except the flexible connecting rod AB, which has length l, mass density ?, and modulus of elasticity E. The connecting rod AB is connected to the crankshaft and the slider block by means of revolute joints. For simplicity, the superscript that indicates the body number will be omitted in the discussion that follows with the understanding that all vectors and matrices are associated with the deformable connecting rod.
The displacement field of the connecting rod is assumed to be
where u f = [ u f 1 u f 2] T is the displacement vector, S b is the shape matrix defined as
? = ( x/ l), and the vector of elastic coordinates q f is
in which q f 1 and q f 4 are the axial displacements of the endpoints, q f 2 and q f 5 are the transverse displacements of the endpoints, and q f 3 and q f 6 are the slopes at the endpoints. One may observe that the...
