11.1.2 3D Constraints

There are only four 3D generalized coordinate constraints. The wide variety of standard 3D constraints cannot be meaningfully converted to generalized constraints; only constraints that attach exactly two bodies together such that only one or two degrees of freedom remain between them are generally useful.
The arguments given to the generalized coordinate constraints are of the same form as the arguments given to the standard constraints. However, each of these constraints requires additional arguments to specify the names of, and an initial guesses for, the new symbol or symbols that represent the added degrees of freedom.

The 3D generalized coordinate constraints.

Note that there is a clear distinction between a master and slave bodies. The slave body is the one that will be represented by the single new generalized coordinate. Thus, the slave body cannot be the ground body. The master body may be the ground body, another body represented by standard coordinates, or another body represented by generalized coordinates that was created with another generalized constraint. The master-slave relationship cannot be circular; the master-slave chain must eventually lead back to the ground, or to a standard body.
Another restriction on the arguments to generalized coordinate constraints is that the axis objects, axis1 and axis2, must each be defined entirely on a single body. While standard constraints allow axis objects to span multiple bodies (such as a line originating on one body and ending on another) generalized coordinate constraints do not.

Example

The following example shows a standard constraint and a generalized coordinate constraint that could be used to perform exactly the same function in a model.

Here are two functionally equivalent constraints.

In[6]:=

Out[9]=

Out[10]=