A Comprehensive Numerical Study on the Number of Identifiable Kinematic Parameters of Parallel Mechanisms

Kinematic error model plays an important role in improving the positioning accuracy of robot manipulators by kinematic calibration. The identifiability of kinematic parameters in the error model directly affects the positioning accuracy of the mechanism. And the number of identifiable kinematic parameters determines how many parameters can be accurately identified by kinematic calibration, which is one of the theoretical basis of kinematic error modeling. For serial mechanisms, a consensus has been reached that the maximum number of identifiable kinematic parameters is 4R + 2P + 6, where R and P represent the numbers of revolute and prismatic joints, respectively. Due to complex topologies of parallel mechanisms, there is still no agreement on the formula of the maximum number of identifiable parameters. In this paper, a comprehensive numerical study on the number of identifiable kinematic parameters of parallel mechanisms is conducted. The number of identifiable parameters of 3802 kinds of limbs with different types or actuation arrangements are analyzed. It can be concluded that the maximum number of identifiable kinematic parameters is $Σi=1n$ 4R_i + 2P_i + 6 − C_i − 2(PP)_i/3(PPP₁)_i/(2R_i + 2P_i)(PPP)_i, where C_i represents the number of joints whose motion cannot be measured and n denotes the number of limbs in a parallel mechanism; (PP)_i, (PPP₁)_i, and (PPP)_i represent two consecutive unmeasurable P joints, three consecutive P joints in which two of them cannot be measured, and three unmeasurable P joints, respectively.