In this post, we consider the detailed application of the principles set out in Part 1 to the analysis of dynamic forces in a Trammel mechanism. The trammel is a very simple machine which has the benefit that the kinematic analysis is uncomplicated, but at the same time, it requires all of the steps discussed in the introductory post.
Not surprisingly, the trammel mechanism motion is governed by a highly nonlinear differential equation, and the prediction of accurate forces requires that this differential equation be solved to accurately describe the motion as an input to the force calculation. The differential equation of motion, giving the angular acceleration of the system without reference to all of the internal forces, is available from Eksergian’s equation of motion. It can be solved numerically by means of the Runge–Kutta algorithm to produce the system motion for any prescribed starting conditions.
With the system motion known, in particular, with the angular velocity known at each value of time and angle, then the force solution can be made as described in Part 1. For the details, see the full article in PDF at the link above.
