Question

This assignment pertains to the planar fourbar mechanism illustrated here. Link 1 is the ground link and includes points O2 and O4. Link 2 connects points O2 and A. Link 3 is a rigid body with moving pivots at points A and B, and Point P is another fixed point on Link 3. Link 4 connects points O4 and B. A 2-D Cartesian coordinate system is fixed to ground with its origin at O2.

This assignment pertains to the planar fourbar mechanism illustrated here. Link 1 is the ground link and includes points O2 and Os. Link 2 connects points O2 and A. Link 3 is a rigid body with moving pivots at points A and B, and Point P is another fixed point on Link 3. Link 4 connects points O4 and B. A 2-D Cartesian coordinate system is fixed to ground with its origin at O2 The fixed distance between points O2 and 04 is Li 2.2 m. The fixed distance between points O2 and A is L21.0 m. The fixed distance between points A and B is L3 2.1 m. The fixed distance between points 04 and B is L2.4 m. The fixed angle Bbetween line segments AP and AB is p-30 The fixed distance between points A and P is Lp-3.1 m. The mass of Link 2 is m2 10 kg, uniformly distributed. The mass of Link 3 is m 100 kg, uniformly distributed. The mass of Link 4 is m4 20 kg, uniformly distributed. The applied force F 100 N always acts straight down at point P The center of mass of Link 3 is located at its centroid G3. The mass moment of inertia of Link 3 about Gs is IG120 kg m2 Link 2 and Link 4 are very slender rods (for calculating Ioz and Ic) A motor at O2 (not shown) applies a torque on Link 2. 82 (Image adapted from Design of Machinery, 5th ed. by R. L. Norton, 2012, McGraw-Hill) At a given instant Link 2 has angle 6270°, angular speed 1 rad/s, and angular acceleration a 2 rad/s2, and the following results are to be determined. Final answers are to be summarized on this front page, with intermediate work shown on attached subsequent pages. There are many intermediate values, which class members are welcome to compare values with each other while independently solving. However, work shown is expected to be original for each individual (e.g, merely copying spreadsheets, software code, or raw answers is cheating). Requirement 0, the angle between line segment AB and the x-axis a, the angle between Link 4 and the x-axis o, the angular speed of Link 3 (+ Ccw, - CW) eas, the angular speed of Link 4 (+ CCW,-CW) Point s rad/s rad/s , the angular acceleration of Link 3 (+ CCW,-CW) aa, the angular acceleration of Link 4 CCW, - CW) G, , the position vector to point B from center of mass of Link 4 pG, , the position vector to point P from center of mass of Link 3 äg, , acceleration of center of mass of Link 2 ác, , acceleration of center of mass of Link 3 a, acceleration of center of mass of Link 4 Neat and clearly labeled free body diagrams for Link 2, Link 3, Link 4 (on attached pages) Equations of motion (F-ma,M-l)for Link 2, Link 3, Link 4 Assembled matrix equation for linkage, with all numerical values entered.(on attached pages) m/s20.5 m/s20.5 (on attached pages) Reaction force at joint Oa Required external torque Ti2 on Link 2 that achieves given motion. Total points possible:

Can you solve all of it please?

Answer 1

22.2m (link 1) AB 2-1m (link 3) 482.4m (link 4) mlOk T24 d2 3 look Now, at a qiven instant- 2 (a) to ind O ie angle betuween AB omd the X-avix :. amale made bu Jink 3 amd -axu 2 2 20 3 50 Am de by link 4in -the z-axi anqle ma (o, A) AB + oB2.AB o, Bes(os) .Cas o5 angle behween B amd

→ (24)2-2x 2-1 x 2,4 cos(es)- (1 )4(22) (2-1) . 2x1x2ㆎ Cos70 ·→ 5.966 2x 2.lx 2.4 55-10 15 Am (c) to tind w3 amqular speed d link from f-Cent mcthae 1x (02 A +2AB s'n (45) 3 @gx(c24 B+ A B) 26 (2.y+2.1 4.5 d) To ind W again Lu 3.2 O 03:25 Yad/s (ccw)