Pinion-rack dynamical model: Newton equations, equivalent mass/moment of inertia, reaction force

Antonio Sala, UPV

Difficulty: ** ,       Relevance: ,      Duration: 15:31

Summary:

This video discusses the dynamic modeling of a rack-and-pinion mechanism with one mechanical degree of freedom.

Newton’s equations (force balances, including reaction force) and the kinematic constraint linking linear and angular displacements (and, subsequently, velocities and accelerations) are presented.

With that complete model, two equivalent simplified models are then presented, either seen from the gear side (equivalent inertia) or seen from the rack (equivalent mass) side. Indeed, since the model only has 1 degree of freedom, everything can be reduced to an equation of order 2 of equivalent mass or inertia times linear or angular acceleration, respectively.

The final part of the video calculates the reaction force between the rack and pinion, both in equilibrium (zero acceleration) and out of it.

An equivalent approach based on Euler-Lagrange with constraints formalism appears in video [pinionELEN].

*Link to my [whole collection] of videos in English. Link to larger [Colección completa] in Spanish.