There are basically two forms of mechanical system, Cartesian systems where the axes are orthogonally aligned with X,Y & Z space for example a gantry robot and non-cartesian systems where the axes are not aligned with X, Y & Z space e.g. hexapods or Stewart platforms.

Inverse Kinematics is the mathematical process of turning X, Y, Z positions into motor positions. In a Cartesian system this process could be as simple as applying a scale factor turning mm into encoder counts while in a non Cartesian system complex mathematics could be required.

In Delta Tau's Turbo PMAC, the inverse-kinematics algorithm is implemented in a dedicated program buffer for the coordinate system. The inputs are the desired platform pose coordinates and the outputs are the command positions for the motors. Turbo PMAC automatically calls the inverse kinematic program buffer for each programmed end point on point-to-point moves and for each “segment” on path-controlled moves (linear and circle mode), typically about every 10 milliseconds.

A simple cubic-spline interpolation between these segment points is computed at the servo-update rate, typically about every 400 microseconds, providing a smooth and accurate approximation of the exact path. There is a trade-off between computational requirements and path accuracy in selecting the segment spacing, but in almost all cases, sufficient accuracy can be achieved at reasonable computational load.