Question

The oil field pump in figure below is designed as pinjointed fourbar linkage. The output link 4 is oscillating when the input link 2 is rotating about Os. The motion of link 4 lead the motion of the cables attached at points P1 and P2 and entering in the oil well PRECTORECTIVE Find the angular velocities of links 3 and 4 and the linear velocities of points AB and Pl in the XY coordinate system for the linkage in the position shown for the two angular velocities w21 rad/sec and = 10 rad/sec Assume that @ 45' in the XY coordinate system and. The coordinates of the point Pi on link 4 are (11468.33.19) with respect to the xy coordinate system. 51,26 STEPS 1. Put all equations needed for design and calculations 2. Put all steps of the calculations including calculations of different constant and parameters) (If calculations are made using a code please add the code)

xy on point O2

Answer 1

Given data Link lengthe:- Link 2 (03.40 A) : a:14pm Link 3 (A to B); b-8097. Linky (OH to b); C-51-26 in Linki ( x-offset); dx = 47.5 in linki (V-offset): dy=(76in-12in). Couplex Point of offsel; Pue=11468 ini coupler point y-offset: Py: 33:19 im. Gant angle Ozxy = 45° Coordinate transformation angle 8-1265820. Input Crank angulaš Velocity W2 = 10 sad's cow. Toro 727570 +51580

Transform the crank angle from global to local coordinade System 82: Bzxy-8-45°-126.5820. --81-5820 Distanice 0204 i do detto in )2+(76n-121n) 2: d = 79.71in the values of the constants meeded for tinding Determine SU K: 579701-5-6929. kid. 79.701 - 15548 51-26 K3 = 026²7c27d2. - 200 = (14)2-(80347151.26)7 (49.0112 2014) (5126). - 196-6;400+2624.5+6242.580 1,435.28 301-3301 7,435.28 - 1.9340 A: COSO 2-K1-K2 Cos 02 + K3 .603(-81.5820) -5.6924-1.5548 Cos (-81-5820)+19340.

: -3.8401 B: -2502 2-2 Sin (-815820) 19485 C: K.-(Katıl.coS02+K3 =569290(15548+1) COS (-81582°)+1934º. 34.2529 lind value of ou for the coassed circuit B4 = 2 Calam 2 (2A, =B+/82.42c ) -262.4820 Delermine the values of the constants needed for finding 03 ku: d= 79.7010 19485 -0.9963 K5= c²d²-a3b² zab. - (7.2529)-(49.701)2 83-8401) 2 (1998512 21-38401) (19485 ) 5-4.6044 Da CoS O2-KitK4 C0382 +k5 = COS (-81-5820).5692970.9963 Cos(-815820)+(-4.6044) :-100081 &=-2sind =-2 Sin(-815820) = 1.9485

Foki+(Ky - 1) cosez+ ks 25-6929+109963-1) COS(-81.5220)+(-46044) 310849. tint value of oz for the crossed Ciscuit Brza 2 latama (20,-€ +/6240F. = 2(19340 famz (26-100031), -4.9495561978: 12746-100021) (1.0849) - 332.4450 Delermine the angular Velaity of link 3 and 4 az: Qwz. Sin (04-02) Sin (03-04) W3 = -0.511 &adls Wy = awz. Sin(82-83) Sin(04-03) Wy.- 2-353 gadis Determine the Velocities of Points A and B. VA -AW2 (-Simas + jcas82) - (138-492720.495.j) imis = {140 inls OvAxy - Arg (va)+8 - 140+126.582

@VAXY = 1350. VB : (wy (-SinOiftjcosou) = (119588-15-781j) inte (VB = 120-624 inks overy - ang (ve) + 8 =119.0642. Distance from Oy to pi es J Per-212-4842 = 48.219 in Su = 180-alum ( Py) 136.5030 Delermine the Velocity of Poini , VP,= Owy (-Sin ( 84+8)+jcos(84481) = (-55422499:1813) inds VP. = 113.469 ins? Pad exPxy : argupit8 -113.469 +126:582 -245-6460.

→ For We = 1 stad is the stank angle from global system : - de Ou Td = 79.701 in) to Transform Coordinate Distance local > All constants volwer K. Kaikz A, B, C, are same as prevines. (fort finding ou) » All constant values Ky, KS , D,E,F are also same as previous case. (fost finding 03) * Determine the angular velocity of link 3 94 We a awe sin cou-02) - sin(0, -01) 63 = 14 X1 sin (262.482°+ 81.582) 80 sin (332.475°– 262.4829) FWs = -0.0511 vod/secy Wu= aw, sin (02-03) Wu-aw in (04-03) Sesy = 0.2353 rad /sec? Determine the velocities of point A and B. VA = aw2 (- sin Oz + g cos 02) VA = 1481 (- sin(-81,582) + jcos(-81,582)] VA = £3. bug + jx2.0495 VA = 13. 99 98 inls { VA = 14 l/89 OVAXY = Wy (VA) +d =8419 +126.582 = 1350