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I must calculate the inverse kinematics of a machine in which one of the joints is constrained to a curvilinear path.

I looked for existing libraries to model the problem, but none of them seems to offer support for such kind of joints. In particular I looked ad KDL, but it only allows movements on a straight line (with a prismatic joint) or on a circle arc (with a rotational joint), but not on arbitrary curves.

Are there any tools suitable for such system that could be used instead of a handwritten solver? I would be interested in particular to libraries in C/C++.

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You can convert between curvilinear and cartesian coordinates no problem. If you are using cylindrical or spherical coordinates, you can choose a convention and convert between the two.

If you are concerned about arbitrary curves, model your joint as multiple joints with extra constraints. There is nothing wrong with breaking down the problem into sub-problems that are easier to solve. There is no need for KDL. I like to use Eigen for my implementations, but prototyping in Python with Numpy should be enough of a start.

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