PROBLEM $3(35$ Points$)$:

In the six$-$link mechanism shown, it is required to find the joint reactions and torque $T_{12}$ when a specified load $F_{16}$ acts at link $6.$ Gravitational, frictional and inertial effects are negligible.

The joint variables are ${}_{12},{}_{13},{}_{14},s_{45}$ and $s_{16}$ as shown. The fixed link lengths are $A_{0}Q=a_1,D_{0}Q=b_1,A_{0}A=a_2,AB=a_3,BC=D_{0}D=a_4,DC=b_4,GE=a_6$ and $HG=b_6.$

a$)$ Using the link figures given below draw the free body diagrams of the links.

b$)$ Write the necessary equations for each rigid body from which the joint reaction forces and T$12$ can be solved in terms of F$16,$ the joint variables and the fixed link lengths.