6.7 Section 6.7 An Example of Closed-Form Dynamic Equations 189 AN EXAMPLE OF CLOSED-FORM DYNAMIC EQUATIONS ulator shown in Fig. 6.6. We assume that the mass distribution is extremely simple: Here, we compute the closed-form dynamic equations for the two-link planar manip- All mass exists as a point mass at the distal end of each link. These masses are m1 and m2. First, we determine the values of the various quantities that will appear in the recursive Newton-Euler equations. The vectors that locate the center of mass for each link are 1Pc = 4, and 0.10.02Pc=1282. Because of the point-mass assumption, the inertia tensor written at the center of mass for each link is the zero matrix: C = 0, C212 = 0. There are no forces acting on the end-effector, so we have f3 = 0, n3 = 0. The base of the robot is not rotating; hence, we have @0 = 0, zwolle wo = 0. m2 S T2 mi FIGURE 6.6: Two-link planar manipulator with point masses at distal ends of links.