Answer Happy

Q5. Analytical Synthesis (8 points) (a) True or false: Assuming the diagram represents a three- position analytical synthesis problem, the length of vector W, is always the same as the length of vector W 3. (1 point) (b) Write the right-side dyad vector loop equation that includes the vector P31. While any legitimate vector loop could potentially be helpful, this question asks specifically for the one that directly assists in analytical linkage synthesis between positions 1 and 3. (2 points) Ps 23 A3 03 M P31 082 22 Ws B₂ 2 J 5 Pa 53 • B₂ to N 21 P21 (23 P₁ 032 B M U₂ 72 2 S A 5 U₁ Y2 (c) Now rewrite the same equation using complex numbers. Use the lowercase expressions for lengths ("U" is the length of U, "p3r" is the length of P31, and so on). (3 points) (d) The two distinct vector loops relating positions 1 and 2 and relating positions I and 3 (both considering only the right side of the mechanism) would produce 12 variables: u., B. B. B. s. 8. 82, 83, P21, P31, B2, and . Assuming that 6 of the variables are specified in the problem statement: (a) identify how many independent scalar equations are available from these two vector loops to solve for unknowns, (b) identify how many "free-choice" variables remain. (2 points)