Problem $(9)$

A planar linkage mechanism is drawn to scale $m_L=10c\frac{m}{c}m.$ In the position shown, link $2$ has constant angular velocity of ${}_2=24ra\frac{d}{s}CCW$ and link $7$ has constant angular velocity of ${}_7=22ra\frac{d}{s}CCW$

a$)$ Prove that the mechanism has $2$ DOF.

b$)$ Draw complete velocity and acceleration diagrams for the mechanism and hence determine ${}_3,{}_6,$ and ${}_3,{}_6,$ as well as the relative velocity $(v_r)$ and relative acceleration $(a_r)$ of slider $5$ with respect to link $3.$

$($Each diagram has to be drawn in separate page$)$

Use the scales: $m_v=100cm\frac{s^{-1}}{c}m,$ and $ma=1800cm\frac{s^{-2}}{c}m.$

$O_{2}A=25cm67$ cm $78$ cm $35$ cm