We present a method for kinematic calibration of open chain mechanisms
based on the product of exponentials (POE) formula. The POE formula r
epresents the forward kinematics of an open chain as a product of matr
ix exponentials, and is based on a modern geometric interpretation of
classical screw theory. Unlike the kinematic representations based on
the Denavit-Hartenberg (D-H) parameters, the kinematic parameters in t
he POE formula vary smoothly with changes in the joint axes, ad hoc me
thods designed to address the inherent singularities in the D-H parame
ters are therefore unnecessary. Another important advantage is that si
mple closed-form expressions can be obtained for the derivatives of th
e forward kinematic equations with respect to the kinematic parameters
. After introducing the POE formula, we derive a least-squares kinemat
ic calibration algorithm for general open chain mechanisms. Simulation
results with a 6-axis open chain are presented.