2.4.2 Constraints

The actual constraint expressions that are generated by SetConstraints can be extracted with Constraints. Constraints can be very useful for debugging a model because it is often possible to read the constraint expressions directly and relate them to the function of the model.

Constraints function.

This loads the Modeler2D package.

In[1]:=

Consider the 2D crankshaft-piston model of Section 1.2. This model is built with various settings for the options for SetConstraints to show their affect on the resulting equations.

Here is the crankshaft-piston model rebuilt.

In[2]:=

The first constraint cs[1] is a two degree of freedom constraint that constrains the origin of the crankshaft to lie at the global origin.

Here is the expression generated by the Revolute2 constraint.

In[11]:=

Out[11]=

Obviously, when these two expressions are driven to zero, the desired result is achieved, the coordinates of the local origin of the crankshaft {X2, Y2} are zero.
The third constraint cs[3] is a two degree of freedom constraint that allows the piston to translate along a vertical axis, but constrains its rotation and its translation in the X direction.

Here is the expression generated by the Translate2 constraint.

In[12]:=

Out[12]=

The first expression, 10 Sin[3], constrains the rotation of the piston; this expression can be equal to zero if 3 is any integer multiple of . The reason that the solution 3 -> 0 is found is because the default initial guess is 3 -> 0. If a different initial guess were used, such as 3 -> 3, the model would converge to 3 -> N[] instead.
The second expression in the list constrains the X coordinate of the piston to be zero. Notice that at any value of 3 that satisfies the first expression, the second expression reduces to or , either of which will drive X3 to zero.