Consider the (RPP) and (RRP) type articulated robot arms given in figures. Assume that the variable of interest is Xc(Ro), the position of the point C located at the extremity of the end- effector, expressed in the base frame. 1. Draw the 3D workspaces of the mechanisms for the following joint courses: RPP: -90° 90°, 0,5m sh≤ 2,5m, 0,5m Sr≤ 1,5m RRP: -120° << 120°, -30° ses 60°, 1m sr≤ 2m (Use a software for 3D views or give the front, side and top views in 2D) 2. Draw the kinematic chains with reference frames attached to links and define all variables and constant parameters. Consider the generalized coordinates as follows: RPP: 91 92=h, 93 = r RRP: 92 =0, 93r 3. Derive the forward geometrical models of the mechanisms such that Xc(Ro) = f(q) by using (3x3) rotation matrices. 4. Use the (4x4) homogeneous transformation matrices with Denavit-Hartenberg parameters and obtain the forward geometrical models. Clearly show all computations and give the table of D-H parameters, i.e. 8. d,, a, and a. 5. Compare the geometrical models obtained in (3.) and (4.). 6. Obtain the inverse geometrical models. Consider the joint courses given in (1.) and comment on the mathematical inversion. Discuss the singular configurations. RPP RRP