Question

Create a MATLAB code to solve the following problem using the cycloidal displacement method discussed in the notes. Generate the SVAJ plot, and be sure to label each plot. Design a double-dwell cam to move a follower from 0 to 2.5 in in 60 deg, dwell for 120 deg, fall 2.5 in in 30 deg and dwell for the remainder. The total cycle must take 4 sec. Plot the s vaj diagrams.

please help

Answer 1

Dwell I Color Quiven data Rise Dwell Fall B = 60 deg $2 = 120 dag & 30 dag En = 150 dog cycle time, t=4 sec h = 2.5 in h2=0 in. h3 =2,5 in. h=016. A) The camshaft tuons 277 xad during the time for ove cycle. Thus tas speed is = 271 rad 27 = 1.571 Brad/set, B) The metion Program with lowest acceleration that does not have infinite jesk is the medifted trapezoidal. From the table the constants C, to ci are defined. C;= 0.388984985 C2=0.0309594; C3=4,888124; (426),425769 C5=2.49406184367 -0.22203094; Cy=0.00723407; C8 = 1.6110154 C9=-0.3055077; GO = 4.6660917; C =-1.2292648 c) the equations for the rise or fall interval (S) are divided into 5 Subinderwals, These are oso = 8/8, fon these Bisa local coordinate that ranges from o to By S; (@,Bah) = n(2, ta sa(979); V(BH)=c} (-ces(273) B² Az B? ay (@,83h) = Cz by sin (2013) ; J, (9,86) Com the cos (1971) Fon 8/8€0 € 39/8 then sa (3,9") -h 5 +48 +3] ; 4, 6,386) 4 (59 70) ( 6, 8, h) – Coz the ; F, O.Bh) = 0 in. For 3/5 0 < 58/s' them S; (0,84)= h (Geo +6 Sia(479_7)+c9) V3 (0,8,1) = (Cp - C, Ces (1972-17) ag ©.8%) = 6s sia(17.8-7); Tz (8.8.)=cythe column --> Fon 5/8 = 0 <78/'ther, su ©,P.b)="[-C568)36 +61); V(33.5)*6*$+) Qr (0,8h)=-C3% ; t (686)=0 in Joh 78/8 2028 $:(@, b)=(2, 1951w (- 370)79-); 6 lepk)-c,(res fong -37) as(0,84) ---, B 38a (476-77) ; TfO,Bh) - combina coes (-3 page of of 03

over the The above equations can be used for a mise en fall by himsending the propen vanhoes of OB and h. To plat SVAT CLONes, Aust define a range function that has a varie of one between the values of a and b and zes else abere. Reza,b)= 14 (co>a) (p<b1,0) E) The Global SYAJ equations are composed of four internas (hise, dwelfalland dwell) The local equations above must be assembled into a single equation each fons 3, X, A and I that applies range O<OŚ 360 60 degrees f) The global equations SVAT for the first intenval,050¢ B. for this internal the local and global frames are chaciénd so the local equations can be used as written, multiplied by the rangé furetion so that it will have non Zeno values oply over its fone so<B, S,(C)= R(0,0.dez.). S(0,896) +POS, 2A)-5,128,6).... + ROZAFB) S (@8,4)+ROFAZA)-Sy@fgh)... +R60, 738 , 8). 5 s (0, 8 , h) V, ©= R(0, 0deg, B).x,(2,8%yho)+R/6, 9278.). vz (2.936). +R/0,3A, ) (@8, 4)+R/0,878) V4 [ 8, 6). +R(0,5 P,B,). Ys (0,31hi) Hi () = R(0,0 deg.£).2,(0,86 , ) +R ,*, 38).az (@,9, b)... som b). ag(0, 8., ho)+R (0,59,3%). ay /B, 83h)... +R678,8). as (, 7,hi) 3, O-R(0, dezes). T, (8 8,45)+R(2,4,7.).T; (0,8,4).. +R CO,ZA, 38), 13(0, Bysky) +R (@},376.Jy(9,8sh).... + R107B, 8).Js (0,8, Global SYAT equations for the second Intenval, B, SO=BitB2-fathis interval , the vakle ofs is the value of at the end of the previous fraterval and the valves EVA and J are zeno because of the dwell. 704 B,<o<B+B2: S2(0)=R OM,(B12).sA; V. ()-R/08/B2).0.in. A2CO-RO 2,03+).0.in;()=R (€ 8,(3,182)).. H) Global S VAT equations for the third indenval, BitBi Sos Bitfet Bufon this interval , the local and global frames are not coincident so we must transform the local @ to the global O by subteracting the finst two intervals from it. Note that for a fall, the local equation for ses sült nacted from the value of s at the endof the previous interval while V, A and I are simply nepated. fon BirtB2 o BitBath 1) svas equations for the fourth Interval, Bytbet B: $0$$_+82483 ty, for this interval, the vallies of s, Y, A and I are Zéro because of the devell. page 02 of 03 + R (0, -

notation 3) complere global equation for the displacement and stot it over one of the cars, which is the sum of the four intervals defined above, 9 (O)=s,[0)+52 )+55(0)754(0) ; 620deg, Idez.... 360 deg 3 Displacement Š Displace 2 het, in se), 60 120 180 240 300 360 deg > com notation angle, deg completeplebad equation for the veraéty and plot it oven ove natation of the cams which is the sum of the foun intervals defined above. V = V. () +V2(0)+ V3 [6)+Y/) Velocity & velocity o ve -5 in -10 360 60 120 180 300 240 Oleg, cam notation angle der 1) Complete global Equation for the acceleration and put it even the one Debatieve the cam, which is the simet foem intervals defined above, AO=A, ) Hz[0)+43(0)44p(0) Acceleration A Acceleration, in --50 60 720 360 180 240 300 m) Sleg, cam notation angle, def. TERK, J 500 complete global equation for the Jerk and pletit over one rotatibve the cam, which is the sung the four Interlals defined above, (o)-5), @)+5y(0)+Up© 1000 10) E 500l Jerk, in Soo -10001 120 160 2970 360 e/dagscam włation angle, duga page os of 03