Investigates robot calibration with planar constraints, and in particular the conditions for the parameters of the robot kinematic model to be observable. Mainly multiple-plane constraints for robot calibration are considered. It is first shown that a single-plane constraint is normally not sufficient to calibrate a robot. It is also proven that by using a three-plane constraint, the constrained system is equivalent to an unconstrained point-measurement system under certain conditions. The significance of this observation is that one can use the three-plane constraint setup to successfully calibrate a robot. Simulations have been conducted to verify the theory presented in the paper.