Step 2. Calculation of the Unknown Contact Forces

In this second step, the unknown components of the contact force vector, h, are computed. The dynamic equations of motion expressed in end effector (or operational) space are combined with the contact model at the tip to accomplish this task. As was previously noted, the equations derived for this step differ slighdy for the two classes of contacts which we have defined, but the fundamental method for finding is the same. First we consider a manipulator with a Class I contact between the tip and another rigid body. 

Combining this equation with Equation 5.21 gives  

Note that if it is necessary to model f using the dual basis composed of and V , the same elimination may be carried out using instead. 

The only unknown quantity in Equation 5.56 is the unknown comp Mients of the contact force vector. A solution for may be found by solving the following linear system of algebraic equations  

The dimension of the linear system in Equation 5.57 is nc. Thus, only an Tie X ne inverse is needed to solve for the unknown components of the ccmtact force vector. Once h is known. 

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