How to Calculate the Forces on Linear Carriage

Examine the type of machine you are using. Different machines require different calculations. The typical machine with linear carriage qualities is a long, horizontal bar with a platform that slides across the bar on wheels by means of a pulley.

Find the information for the variables of the linear carriage equation. The key variables include length of the payload mass, including platform and object mass, acceleration rate, vertical distance to center of gravity and the carriage wheel base.

Solve for the wheel axial reaction force based on the following equation:

F = (Mp * a * h) / 2x

Where Mp is the payload mass, a is acceleration, vertical distance to center of gravity and x is the carriage wheel base.

Input data and solve for the force on the linear carriage. Assume the following variables:

Mp = 20 kg
a = .5 m/s^2
h = .4 m
x = .6 m

F = 20 * .5 * .4 / (2 * .6) = 3.33 Newtons