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Constraint-with-Expressions.md

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FreeCAD has a powerful Expression Engine. This tutorial shows how to create simple mechanism using constraints driven by some expressions.

Screw Mechanism

It is very easy to create a screw mechanism with PlaneConicident constraint. Just follow the simple steps below

  • Set the constraint property LockAngle to True;
  • Enter an expression;
    • If you want to drive by rotating the screw, then express the Offset property in term of the Angle property, as shown in the screen cast below;
    • If you want to drive by translation, then express Angle in term of Offset.

[[images/screw.gif]]

Gear Mechanism

A slightly more complex example is a rack and pinion system shown below. All gears have module of 1mm. The big pinion gear has 18 teeth, while the small one has 15. You can download the parts here. You need to install the Gear Workbench if you want to modify the gears.

[[images/gear.png]]

By the look of the picture above, one may intuitively think of using the PointOnLine constraint for the gear in the slot. But in this case, it is much easier to use, again, the all powerful PlaneCoincident constraint. We divide this system into two assemblies for, well, the pinions and the rack.

First, create a sketch to define the positions of the two pinions. In real applications, you probably should derive the distance of the two circle using expressions, too, as well as most of other constants shown in this tutorial, or better, use a Spreadsheet.

Then, create an assembly, add the sketch and two gears, and position the two using the sketch with PlaneCoincident constraint.

Toggle the LockAngle property of both constraints. And since we will be driving the big gear, enter the expression for the Angle property of the small gear constraint as below, which is basically the gear ration with some offset,

-Constraint002.Angle*18/15-6

You can test the mechanism by changing the Angle of the big gear constraint.

[[images/gear1.gif]]

Now, we create the final assembly, add the pinion assembly and the base with the rack gear, and fix them together with another PlaneCoincident. Notice that we are using the Sketch for constraining. This is important, because the gear is meant to be rotated, while the Sketch is fixed. We shall again lock the rotation of this constraint. We want to translate the pinions in its relative Y position, so enter an expression in the OffsetY property of the constraint,

-Constraint001.Angle/360*15*pi

Done!

[[images/gear2.gif]]