Generalized coordinate partitioning for complex mechanisms based on kinematic substructuring

摘要: Abstract Generalized Coordinate Partitioning (GCP), a partitioning of the Jacobian matrix, allows for automatic identification dependent and independent variables primary secondary systems equations constrained multibody mechanisms. The GCP method is achieved through row column permutations associated with applying Gaussian Elimination Complete Pivoting (GECP) to constraint matrices. forms basis robust efficient kinematic path planning solution dynamic motion, potential achieve orders magnitude speed up over least squares iterative methods. Despite these benefits, significant disadvantage that numerically expensive. This paper presents technique automatically rearrange groups intersecting loops into non-overlapping substructures, which effectively block-diagonalizes Matrix. applied hydraulic excavator, an illustrative example complex mechanism, approximate order reduction in floating point operations required perform demonstrated. Numerical results comparing run time substructuring sparse matrix methods full dense GECP are provided. Furthermore, compact representation motion formulated, accounting substructures identified mechanism.