16. Figure 2.17 shows a two degree of freedom manipulator. Let lo, 11, 12 be the link length parameters and 01, 02 the joint angle variables of link 1 and link 2, respectively. (a) Express the position and orientation of frame C3 relative to frame Co in terms of the joint angle variables and the link parameters. lo C 4 C 12 Dost C3 Figure 2.17: A two degree of freedom manipulator. (b) Compute the spatial velocity of C3 relative to Co as functions of the joint angles and the joint rates. (c) Compute the body velocity of C3 relative to Co as functions of the joint angles and the joint rates. (d) Optional: Find the spatial velocity of the origin of C3 and use this to check your answer for parts (b) and (c). You may want to use a symbolic math package, such as the one described in Appendix B, to carry out the computations in this exercise.