Utilization of the Moore-Penrose inverse in the modeling of overconstrained mechanisms with frictionless and frictional joints

摘要: Abstract The indeterminate equations that describe overconstrained mechanisms are often solved using the Moore-Penrose inverse. Some limitations of this approach investigated here. Firstly, frictionless systems considered. problem solvability accelerations and joint reactions is studied—the non-uniqueness uniqueness discussed. Next, dependence results on selection physical units examined. It checked which elements solution physically non-equivalent after changing units; relationships between different solutions derived. Secondly, frictional Joint friction dependent independent normal load studied. Fixed point iterations Newton's method applied to solve nonlinear motion. inverse employed conduct calculations. null space components considered, necessary amendments in iterative processes termination criteria origins Lagrange multipliers analyzed. unit-sensitivity system models addressed. Finally, an illustrative example given, conclusions drawn—limitations possible improvements