6.2.2 Example 2D Gear Mechanism

To demonstrate the use of Modeler2D gear constraints a 2D model is developed that uses a pair of gears, a pair of pulleys and a belt, and a rack and pinion. The input to the model is the specified rotation of the drive gear. This, in turn, rotates the driven gear, which is the same body as the drive pulley. The drive pulley rotates the driven pulley, which is the same body as the pinion. The rotation of the pinion causes the rack to translate.

Here is a 2D gear-drive mechanism graphic.

Bodies

Five bodies are used in the gear-drive model. No body objects are defined because no explicit point coordinates are used in the model.

Names are defined for each of the body numbers in the model.

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Constraints

Eight constraints are required to model the gear-drive mechanism.

Here are the constraints for the gear model.

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Runtime

Initial guesses for the drive pulley, rack, and pinion must be set or the model will not converge. Almost any guesses greater than zero will do.

This sets the initial guesses for the next solution attempt only.

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Because of the presence of time T in the driving constraint, the model can be run through its intended range of motion by varying T directly with the SolveMech command. The numerical value of T specifies the angular coordinate of the drive gear.

Now run the model at T = 0.05.

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Now run the model at T = 0.25.

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Here is the gear-drive mechanism at T = 0.25.