Abstract
This article presents a method to solve the impact of a kinematic chain in terms of a non-linear contact force. The nonlinear contact force has different expressions for elastic compression, elasto-plastic compression, and elastic restitution. Lagrange equations of motion are used to obtain the non-linear equations of motion with friction for the collision period. The kinetic energy during the impact is compared with the pre-impact kinetic energy. During the impact of a double pendulum the kinetic energy of the non-impacting link is increasing and the total kinetic energy of the impacting link is decreasing.
Highlights
Impact is a common and important phenomena in mechanical systems
Kane and Levinson were able to extend the impact analysis and they showed for a double pendulum impacting a surface one can obtain energetically inconsistent results for friction using a kinematic coefficient of restitution [3]
This article presents a method to solve the impact of a kinematic chain in terms of a nonlinear contact force
Summary
Impact is a common and important phenomena in mechanical systems. The simplest impact analysis is based on the conservation of momentum and a kinematic coefficient of restitution defined by Newton. Kane and Levinson were able to extend the impact analysis and they showed for a double pendulum impacting a surface one can obtain energetically inconsistent results for friction using a kinematic coefficient of restitution [3]. Stronge presented a contact model using springs and the impulse at separation was obtained using the energetic coefficient of restitution [6] All these previous research are using algebraic equations for the calculation of post-impact velocities. The previous models did not consider the three periods and we propose a new elasto-plastic force and new permanent deformations for the impact of the double pendulum With this method we solve the post-impact velocities without introducing a coefficient of restitution.
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