Multiple impacts of a planar kinematic chain with a granular matter

Abstract

The theoretical model of a planar kinematic chain with multiple points impacting with a granular matter is studied. The force acting on the links penetrating the granular media is a linear superposition of a static (depth-dependent) resistance force and a dynamic (velocity-dependent) frictional force. A general algorithm for the m impacts for an n planar kinematic chain is presented. The complete solution of a two link chain with two impact points is simulated using different initial impact velocities and different impact geometries. We analyze how rapidly the ends of both links impacting a granular media slow upon collision. For most of the analyzed cases the tips of the kinematic chain under high impact force (higher initial velocity) come to rest faster in a granular matter than the same body under low impact force (lower initial velocity). There are also some exceptions to this rule.