Wolfram Technology Guide: Integrated Geometric Computing  previous | next 
Compute Geometric Transforms Symbolically
Mathematica makes it easy to combine geometric transforms in any number of dimensions--here to compute the motion of a 10-segment planar robot arm.
In[1]:=

Click for copyable input
Simplify[Apply[Composition, 

    Table[Composition[RotationTransform[Subscript[\[Theta], i]], 

      TranslationTransform[{Subscript[a, i], 0}]], {i, 10}]][{x, 

    y}]] // TraditionalForm
Out[1]//TraditionalForm=