The system shown in Fig. 1 consists of a base N and three bars A, B, C. N, A, B, and C are connected by revolute joints at points R, O, P, S. The bars RO, OP, PS, SR have lengths L1, L2, L3, L4, respectively. The right-handed coordinates fixed in N, A, B and C respectively are {N1, N2, N3}, {A1, A2, A3}, {B1, B2, B3}, {c1, c2, c3}. R LA S S1 eN1 1 A2 A1 B2 I2 L3 B1 c2 c1 02 B P N2 Figure 1: Rod on rotating column, for problem 3 (a) Write the vector loop equation FO/R+P/O + S/P + FR/S = 0 in terms of Lj, j = 1, 2, 3, 4; Ni, Ai, Bi, ci, i = 1, 2, 3. (b) Form the direction cosine matrices NRA, NR, NRC (3) (c) Form two scalar constraint equations by dotting the vector loop equa- tion with 1 and 2.