Modified Composite-Rigid-Body

The Structurally Recursive Method is then expanded, and a second, non-recursive algorithm fw the manipulator inertia matrix is derived from it A finite summation, which is a function of individual link inertia matrices and columns of the propriate Jacobian matrices, is defined fw each element of the joint space inertia matrix in the Inertia Projection Method. Further manipulation of this expression and application of the composite-rigid-body inertia concept [42] are used to obtain two additional algwithms, the Modified Composite-Rigid-Body Method and the Spatial Composite-Rigid-Body Method, also in the fourth section. These algorithms do make use of recursive expressions and are more computationally efficient. 

In the sixth section, the computational requirements for the methods presented here are compared with those of existing methods for computing the joint space inertia matrix. Both general and specific cases are considered. It is shown that the Modified Composite-Rigid-Body and Spatial Composite-Rigid-Body Methods are the most computationally efficient of all those compared. 

Four algorithms for computing the joint space inertia matrix of a manipulator are presented in this section. We begin with the most physically intuitive algorithm the Structurally Recursive Method. Development of the remaining three methods, namely, the Inertia Projection Method, the Modified Composite-Rigid-Body Method, arid the Spatial Composite-Rigid-Body Method, follows directly from the results of this tot intuitive derivation. 

Table 3.3 Algwithm for the Modified Composite-Rigid-Body Method...

The number of scalar operations required by each of the four methods presented in this chapto have been calculated explicitly. As a specific example. Table 3.6 lists the computations required by the Modified Composite-Rigid-Body Method for the case of an A -link manipulator with simple revolute and prismatic joints. Note that the computations listed for the transformation matrix, % i, correspond to the use of two screw transformations as discussed in the previous section. 

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