Gear geometry, constraints, and creation

I have a few questions about gears.

Here are some questions from the following sites.

https://jp.mathworks.com/help/physmod/sm/ug/model-gear-constraints-1.html

1．Does the difference in geometry make any difference in the calculation of torque, friction, etc.?

2．Is it possible to reproduce a rack and pinion mechanism like the one in the image? I want the pinion gear to spin without any constraint from the rack when there is no gear.

3．How can I create an accurate gear using MATLAB files and Simulink blocks?

4．How can I reproduce realistic gears with gear friction, inertia, etc.?

I would appreciate an answer.

Answer 1

[Steve Miller]

1. Does the difference in geometry make any difference in the calculation of torque, friction, etc.?

The transmitted force and torque depends on the gear ratio between the pinion and rack degrees of freedom and the mass/inertia of the two parts. If you attach a Rack and Pinion Gear Constraint between properly constrained rack and pinion parts, the geometry only affects the torque/force if the mass and inertia calculations are based on the geometry.

2. Is it possible to reproduce a rack and pinion mechanism like the one in the image? I want the pinion gear to spin without any constraint from the rack when there is no gear.

Yes - simply omit the Rack and Pinion Constraint

3. How can I create an accurate gear using MATLAB files and Simulink blocks?

If you are speaking of the geometry, you can import the parts from CAD or use MATLAB to define extrusions for the parts. See the Simscape Multibody Parts Library for examples.

4. How can I reproduce realistic gears with gear friction, inertia, etc.?

Inertia effects are included automatically. The Rack and Pinion Constraint only implements the constraint between the gear angle and the rack displacement; you would need to add the friction effects yourself, either by adding damping to the joints defining the pinion and rack degrees of freedom or by using the External Force and Torque block.

--Steve

[A]

Thank you for your answer.

I have an additional question.

2．When I use the "Rack and Pinion Constraint" to constrain the rack and pinion, I think the rack and pinion are always engaged and the rack cannot be released as shown in the figure. What should I do?

3．Can I connect the "Spatial Contact Force" to the gears in the Simscape Multibody Parts Library? I would like to know how to do it.

[Steve Miller]

To disengage the pinion from the rack, you will need to connect the Rack and Pinion constraint to a "dummy" part which has a small (but not zero) mass and inertia. Connect that "dummy" part to the gear using a Weld Joint. When the Rack and Pinion should become disengaged, disable the Weld Joint using Joint Modes.

The Simscape Multibody Parts library has example models with gears in them.

[A]

Thank you for your answer.

I didn't understand the dummy connection very well. Sorry about that.

So I made a simple rack and pinion.

Within the red block of the pinion, I want to remove the constraint so that the rack can move upward by the spring.

I would appreciate it if you could fix it.