The microstructure and properties of suspensions of nonspherical particles are influenced by the specific particle shapes through hydrodynamic interactions. We describe algorithms for Stokesian dynamics simulations of arbitrary shape particles, rigid or flexible, constructed with appropriate constraints among rigid spherical particles whose hydrodynamic mobility is computable by various available schemes, including the one that we recently described [J. Chem. Phys. 112, 2548 (2000)]. The optimal algorithm also provides for rigid attachment among particles during simulation, by aggregation for example. Its implementation for a system with a general combination of internal coordinate constraints (available in a routine from the author) is tested in simulations of sedimentation of spheroids and chains in bounded and unbounded geometries.