An algebraic analytical approach for redundant parameter analysis of serial and parallel mechanisms

Redundant parameter analysis is crucial for the kinematic calibration of mechanisms. To address this challenge, the paper proposes an analytical redundant parameter analysis approach based on physical-to-algebraic transformation for both serial and parallel mechanisms. First, since the end-effector error is free to redundant parameters, the problem of redundant parameter analysis for the serial mechanism is equivalently transformed into constructing a basis for the parameter-independent null space of its identification matrix. A direct sum decomposition is applied to the null space at the initial zero-joint-variable configuration. By extracting the redundant parameters within the resulting subspaces and rigorously establishing their completeness, the closed-form solution to the maximum number of identifiable parameters (MNIP) of serial mechanisms is derived. Then, the explicit forms of redundant parameters of parallel mechanisms are also obtained by decomposing the corresponding parameter-independent null space. The analysis illustrates that the MNIP of parallel mechanisms depends on the number of unmeasurable passive joints, joint configurations, and special kinematic configurations. Finally, the proposed approach is illustrated and validated through a case study of a 6-UPS mechanism.