Direct Dynamics for Single Open Chains

A similar 0(N ) method, presented by Angeles and Ma in [2], uses the concept of an orthogonal complement to construct the joint space inertia matrix. The Cholesky decomposition of this matrix is used in solving the appropriate linear system for the joint accelerations. The computational complexity of this algoithm is slightly better than that in [42], but the algorithm is still not the most efficient It, too, is restricted to configurations of simple revolute and prismatic joints. 

Brandi, Johanni, and Otter [3] have developed an 0(N) approach which is v similar to that of Featherstone. The method differs only in its use of a more general joint model (allowing multiple-degree-of-fieedom joints) and in the optimization of vector and matrix transformations. Of all the algorithms considered, this one tq pears to be the most efficient for computing the joint accel tions for an open-chain mechanism. The optimized mathematical transformations are very important, and they may be used in any general application where vector and matrix quantities must be transformed between coordinate frames. 

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