Kinematic Mechanism: Finalterm Exam Sol - Chibum Lee · PDF fileKinematic Mechanism Final Term Kinematic Mechanism: Finalterm Exam Sol ol-lfI·-, "Co' 1. For the aircraft...

Kinematic Mechanism Final Term

Kinematic Mechanism: Finalterm Exam Solol-lfI·-, "Co'

1. For the aircraft overhead bin shown in figure,

(a) Find the mobility. (15pt)

(b) Check the Grashof condition. (15pt)

(c) Check whether the input link 2 and the 17.5

output link 4 are crank or rocker. (20pt) 23.9

,,0\) -::it of , 't ~ ; N - 4.::(:t of ~·o"'-.,,<;·(:Tt;:: et-

.1.-=-0

A~ 'Ql.o o·

(6)II' , 11o~..). + /'76 1::)':1 =: (90.:).2; . r~-= ,:LY.9 )

<;v\C\'t .= Y\_. ~CO.~=~ ..r.s

yr., .= L:}-3.~.1.)-+.J 3,).. 9~ =-- 3:.2<4.. +3 Y4 ~l43.1..::.

s +.Q = ~ 4 Y--.l <.:.. p.~Ls = y:.-\-r-+------------------------------ ~

~ \'lOt'\ <f\ VL>•.'S~cif / FT s-

~(')v\cw\ ~ YC-S hc;f. 7\·-t~A~

( ~~~t ..~k... ~r ) le;

\. c)\k+-~\ I""~ , vv<±"er-

Dec. 16, 2014 1 Chibum Lee

Kinematic Mechanism Final Term

2- The right figure shows a mechanism used in a production lineto turn over cartons so that labels can be glued to the bottom

of the carton. The driver arm is 1.5 m long and at the instant

shown, it is inclined at a 60° angle with clockwise angular

velocity of 5 rad/sec, The follower link is 1.6 m long. The

distance between the pins on the carriage is 0.7 m, and theyare currently in vertical alignment.

(b) Determine the velocity of A, B, and X. (40pt)

'>(a) Find all instant centers at current position. (Write the c ord; a~) value with resp~ct to 0)

/ ~ L~~i.S~( Ll.. Lg-=o.{

L~ '::I- 6Le,(6..) -5:)~~~ (i, .1-) =(0,0) .<f]

S7Z-~t::J.(l, 3) =- (L~c.o~Q..l..1 kSlV\& )

:=: C -61>" ( (. i9C1 ) _I.)',?.

<1~1,~C.LLl) = (Ll.. 0::S9.?- L:~.s~\V\GI.L.- L5),

:::(-0 ·1)'; O.SCt4D) "_ _ J

r~ k-::: L.L.~\V'lO.>.-L3 '::: L4 '5\11\0( .

'" ~ I ~ '~'" ~ ,;\,,-1 (L5':;~ ) ~0,3851 vJ ~ "-/.'ir)l~e~ G~::: 1f-~ )

L,f'

Lt Co$.O\ - L~G:{.Tf~

~:::-tav0~" 2-\-

Y c:: +OM<9~ ( )\ ~ o.~n36) .9-\ jJ2~

(-0. D-3 , a. 386.1). (0

(Gq.Cu5~ + L.Ccs (\. f 0)

- (0. ?ss (}~ Cl)

( ~.4)

------------~. IQ

4 Chibum Lee

vv-'\-~- \ ~ 'Lt-i~,\l~ ,,£~c/"

----~ pc

':5'~-4'--. (t I

c.')..\~ \ \ I[',- -) - - "e.'] - - (.\.1)(<::'''l~-().:uJ)

4.044 \ \1-<,/5. J.. 68. o~e .'._._--._- {O

Kinematic Mechanism Final Term

(a) Find the time ratio Q - ratio between return and

forward motion. (20pt)

800mm3. For the offset crank-slider in the figure,

(b) The 200 mm crank is rotating at 500 rpm, CCWand is speeding up at a rate of 300 rad/ S2. Deter-mine the position x, velocity i: and the accelera-tion of x the piston (10-20-20pt)

z

-d1~

"~ .. ------------------~

0<'+ (-.~ ...-.-----.-.----~

Dec. 16, 2014

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Kinematic Mechanism Final Term

(a) Determine the angular velocity and acceleration of link 4.(30pt)

--·'··60cm'···~ef

LI

4. At the instant, the angular velocity of link 2 is 30 rad/s CCW andthe angular acceleration is 5 rad/s2 CCW.

(b) Determine the sliding velocity of link 3 with respect to link4. (20pt)

=j 2:J::J~ ~() '4 - .y".loXGO'1' c~.s.4 ~ '~ 4-4.;lO~ vv\w\'- S

L-.7). Cl? ~. -I (kS'iv\ <I:>.. )S\\I\(9

4= s;',V't c:f~ ~ U4 =0 5hA cg =28.6 7SjC) ~

b. ~3:.~q~ ~ sz: PeA -+ Rs.c ~f c~<;.~ CfJ;,\·

;p~ 1~L~e. = - Lf-+ CB eoUi c:,," 9&:'" -' ~~ ,'j&

L-~9G.l..e = c.&e +Cg:J~e '~~

L..l.jU)~([os.Q~i-y5irS:..) = CB> (c.use4+j.s'IV\<94)·~ C{3W~(~~'-SIv\~"')

~ [o.se - Ci3.$''''t9.f][C-E] -;::-[ -~W.;.S'I~(9,-]~ s\V\~ c~coA t:0.1 / :LW~ GJ.>E>...).

CB. = - 863. 7/1-7 CiM/~W3 -= - s-, ') ~~3> vof'~

IQ

C. ?~~~ 1~~~ (1) 'ujtL.- -0~ •-'- J& ' . )~1- ' . j~ ~ ••~~ . '~j

L.7).jQ..).~j - L2-<9:ie ~, eRe ,t :J..CRj <94-e ,+ Cgj~-C~D4e..

Cg e~~ CBj(j4 €J ~- LJj(9~r}e~ L.2. o~Jf)~~&j&4t1&t+CBiJ~:"e1cSlt

(c7:f:>& +0s\~~ )CE + cJ?l1Q:)s~'-$:i",6JD<i-

.= L~e..L (j CU$Q.,A - ,S'\V\ (9~) '- 6..EJJ\c'OS&')' + .) S"V\ 6).2.).-xB 64 <] G~5£4-s:-§)·+ Cg~~ (c~sOct.-+ JJ-S_\Vi_' ~--.;,.)~ __

Dec. 16, 2014 4 Chibum Lee

(c:.& .~ l?~g.Lq Cw./.,->-)0( 4-= - 8 f o. 66 4C; yaJ Is~iO-

Kinematic Mechanism Final Term

5. Consider the following cam follower specification: (50pt)rise: rise 20 mm in 1.0 sec using parabolic motion.dwell: maintain the extension for 0.5 secfall-l: fall 10 mm in 0.5 sec using cycloid motiondwell: rest for 0.5 secfall-2: fall 10 mm in 1.0 sec using harmonic motion

(a) Find the angular velocity of cam, wcam.

(b) Draw the rough shape of the cam and denote the angles corresponding to the intervals, re-spectively. (Assume rise start from 00 and use the knife edge follower with base circle radiusr=50 mm.)

(c) Draw the displacement diagram (t vs. h) roughly. Describe the displacement functions for eachof the intervals.

(d) Find the maximum acceleration (absolute value) of rise, fall-l and fall-2 interval.

(0

Cio) --' (a~,gCII e

f) I 4J.C6C1