The Figure 2 shows a two link planar RR robot using MKS units. The links have negligible mass and inertia, but the joint motors do not. There is a force 10 newtons downward applied to the end-effector. Gravity acts in the-yo direction. It is suggested to use the fixed coordinate directions for simplicity and the reduced forms of the planar screw quantities, i.e. 3 x 1 column arrays and 3 x 3 matrices so that the 6 X 6 inertia matrix and shifting matrix reduce to [m 0 0 M = 0 m 0 0 11 [10p(oc)y] p(oc)x 1 (a) Determine the inertias, M.(o,), i = 1,2. (b) Determine the twists Toi (0), i = 1,2. (c) Determine the kinetic energy, KE = KE + KE (d) Determine the joint actions Q* due to the tip force and Q9 due to gravity. (e) Apply Euler's equations Yp2 Figure 1 03 od OKE dt dq 0,X(oc)= 0 1 lo 0 to determine the dynamic model N(q) + C(q. q) =Q+Q* + Q (f) If q = 3,92 = -1 and = -4,42 = 2, determine the joint loads Q. (g) Suppose each motor includes a 6:1 speed reducer. What are the required motor torques Qm for the above specifications? Yo m = 4 1=16 T OKEY 9 Xo =Q+Q* + Q 4 Figure 2 m=4 12=16 3 92 10