Matrix-Displacement–Direct-Element Method for Force and Torque Analysis of Determinate and Indeterminate Space Mechanisms With Arbitrary Skew Angles

A matrix-displacement-direct-element method (a finite-element method with spatial line elements) for elastic analysis of determinate and indeterminate space mechanisms with arbitrary skew angles is presented, wherein each member experiences flexural deformations in two orthogonal planes, torsional deformation about its axis, and axial deformation. A generalized-member external-stiffness matrix is developed that is used in forming the global external-stiffness matrix for the mechanism member by member. The method permits different freedoms of elastic deformation for the ends of links at pair locations about the axes of pair freedoms. It is also for the elastic analysis of space frames having arbitrarily oriented spatial members. Force and torque analyses of the indeterminate 4R Bennett and 4P space mechanisms are performed in the numerical examples; force distributions, deformed geometries, bearing forces, and mechanical advantages are given.