Question

Kinematics: Forklift Opening Swing Door (P) υ r С bl x(t) Р G A forklift G opens the swinging door as shown. Find the velocity and acceleration components of point P for the instant shown in the lower sketch using natural coordinates. Find the acceleration components of P for the case when the forklift passes through the swing door with constant velocity (in natural coordinates). Given: b, r, *(t), v(t)

Answer 1

given positions G 0 Now coolsider thee Loop OAB - simply assign vectores as shown we can A ra @j 0 with angle oa (o ta is forom o to A and making an angle o, Cero tve a-apie in cow direction. Para s from A to B and making an with the araxie in cow direction. Es is from oto B and making an with the acaris in eod directeson angle og Lig les constant Changing in onagonitude foc constant. ana erg is constant. Scanned with CamScanner

writing 561 rge so + These Toeges can obtain! one f i elog Ez eloz + Isjes e jog icg sine tregutze I rsl is changing f biz is changing, writting a simple vector loop equation ! + F = Fz; * Og a tant mi hotel hence a known quantity. in complex form'- Ra Rejo. of Differentiating gelas jagagesos = V(t); known quantity jcose Imaginary, imaginary, separating the above imaginary iz singa . a Bolts rigol constant. rige jag Cina. jejo eio Caso + = Jaime OSD-sino. sreal 6 real imaginary coefficients :- Scanned with CamScanner

(ooksprms are co (- @ng t ѕид од 3 га <iv6, . { separating the real co-efficients : на софра e, Cog Bg - fosimp3 o Es Casa та з 89 & Case forom method of determinant we can easily solve for the conknowns. #in82 rg Cose, (0g Л О» 2. - зі?е, - TC2 Costa (3 %те, - 14 ") Rz Costa Itaine, 2 - <imensiya os Case Cost3 — Г San10 t, Cos.b, Cosos. Cog 02 + sind. Sind, 2. - &ars (с — без Ces (en- 03) Erg Cos (02-63) rez Cas (02-03) Drez is 2 2 -Та Scanned with CamScanner

Auz= sine rezsimon are Casa Sindz-ren sind, Caso recoso Caso3. azil singog. Cosby - Simon.costa Eq sin (03-02), rég sim (83-62) Eg sin (02-03 Duz Wz - rez rez we got a (= Angulare relocity of link 3 Velocity off point $? - uzrc lèg sin@a-es)x 2 x fС rez 2 M 62 Vejresin (90-tamil.) Tz + Ct) √6² +2(t)? Tag Vit) os = fan ь 2(t) Again differentiating the velocity equation (4) !- of Egejoza üzejo tres joge je tjeguze 103 + ji reg dog ejes + jo regwajéges of Give constant velocity; esos izejaz tjalne wgejo tj redzejaz igweed Scanned with CamScanner

rij e jong + j arguge jeg tjagdge in - -0. ige's Unknowns rez 8 23 ; oy tj Rreg wg eld3 + jezdze (03 - reg wees Separeating the imaginary co-efficients Dy tëz sin 63 t grég W, cas og 7 Rady cosog arguz? sino con sy iz sin oz & Izd 3 Cost; = RZW}} sinag-ar2W3 Coso, Separcating the real co-efficiente a) Escosa, 2rez Wz sin oz-regdzsina; - rezu? Case3=0. icz casoz - Izda sino3 Raw} co503 + 2r6 g Wysings. -2 By deferroniozagt melhods Sinoz Is cosa TG Cas? -tez sing, =p no3 riz sint 2 Cos 03 3. e sinos Da q sina - Plest, q Cosoz Дез d3 - where q sinoz-Plosos -R3 P=tegwa siolog - 216gWgleses q = raw caso3 + 2iig uz sings Scanned with CamScanner

Now we gote the expression for da; w²r. dk = at net accelereafton of point p' = 1 Qra)? + W76 At = tangential acceleration a Qt = dir. 22d3; groomal freadial accelereation (@n) austre, Scanned with CamScanner