Question 11.2: Dynamic Force Analysis of a Threebar Crank-Slide Linkage wit...
Dynamic Force Analysis of a Threebar Crank-Slide Linkage with Half Joint. (See Figure 11‑2.)
Given: The 5-in long crank (link 2) shown weighs 2 lb. Its CG is at 3 in and 30° from the line of centers. Its mass moment of inertia about its CG is 0.05 lb-in-sec². Its acceleration is defined in its LNCS, x,y. Its kinematic data are:
\begin{array}{cccc}\theta_{2} deg & \omega_{2} rad / sec & \alpha_{2} rad / sec ^{2} & a_{G_{2}} in / sec ^{2} \\60 & 30 & -10 & 2700.17 @-89.4^{\circ}\end{array}
The coupler (link 3) is 15 in long and weighs 4 lb. Its CG is at 9 in and 45° from the line of centers. Its mass moment of inertia about its CG is 0.10 lb-in-sec². Its acceleration is defined in its LNCS, x,y. Its kinematic data are:
\begin{array}{cccc}\theta_{3} deg & \omega_{3} rad / sec & \alpha_{3} rad / sec ^{2} & a_{G_{3}} in / sec ^{2} \\99.59 & -8.78 & -136.16 & 3453.35 @ 254.4^{\circ}\end{array}
The sliding joint on link 3 has a velocity of 96.95 in/sec in the +Y direction.
There is an external force of 50 lb at – 45°, applied at point P which is located at 2.7 in and 101° from the CG of link 3, measured in the link’s embedded, rotating coordinate system or LRCS x’, y’ (origin at A and x axis from A to B). The coefficient of friction µ is 0.2.
Find: The forces F _{12}, F _{32}, F _{13} \text { at the joints and the driving torque } T _{12} needed to maintain motion with the given acceleration for this instantaneous position of the link.
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