Gear Trains

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Summary

This video leads students through using linear algebra to model a gear train. This is achieved by modeling each rigid gear body as a system of 3 equations, the input and output gears as one linear equation each, and then modeling the connection between gears as another linear equation derived from Newton’s second law. The resulting matrix is explored for consistency and design elements.

Learning Objectives

After watching this video students will be able to:

  • Model the forces and torques in a gear train as a system of linear equations.
  • Combine these linear equations into a matrix equation.

Funding provided by the Singapore University of Technology and Design (SUTD)

Developed by the Teaching and Learning Laboratory (TLL) at MIT for SUTD

MIT © 2012

Related Resources

Instructor Guide

This resource may not render correctly in a screen reader.Gear Trains Instructor Guide (PDF)

It is highly recommended that the video is paused when prompted so that students are able to attempt the activities on their own and then check their solutions against the video.

During the video, students will:

  • Explain how a matrix equation is modeling the force and torque balance on one rigid body gear consisting of two gears molded together.
  • Work out an analogous matrix for another gear body whose free body diagram is given.
  • Write a linear equation that describes the torque balance due to the gear attached to the motor.
  • Write a linear equation that describes the torque balance due at the output gear.

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