Miscellaneous Problems. pinned to the ground

Transcription

1 Miscellneous Problems Problem. Use the mobilit formul to determine the number of degrees of freedom for this sstem. pinned to the ground pinned to the ground Problem. For this mechnism: () Define vectors for constructing vector loop; show their ngles with respect to the horizontl -is; write the vector loop eqution. (b) Write the corresponding lgebric equtions. (c) Tke the time derivtive of the first lgebric eqution (component eqution onl; there is no need to tke the time derivtive of both equtions). (d) Show the corresponding ccelertion eqution (-component eqution is sufficient). Problem. The link lengths of four-br mechnism re given s listed in the tble (our choice of units). () Drw the four-br in the configurtion where the trnsmission ngle is t its mimum. Wht is the ngle of the crnk t this configurtion? Links L1 (ground) 5.0 L (input/crnk) 1.0 L3 (coupler) 4.0 L4 (follower) 3.0 Lengths (b) On the sme digrm, drw the four-br in its other configurtion where the trnsmission ngle is t its mimum nd the crnk ngle is the sme s in (). Problem. For the mechnism shown the following constnt lengths re given: = 1., = 1.0, = 1.5 () Construct vectors on the figure nd show the ngle for ech vector. (b) Construct the vector loop eqution. (c) Write the necessr lgebric position equtions. (d) Wht re the vribles in these equtions? (e) Write the lgebric velocit equtions. (f) Write the lgebric ccelertion equtions.

2 Problem. For this inverted slider-crnk mechnism, the necessr vectors for nlticl kinemtic nlsis re provided. The vector loop eqution ields the following lgebric equtions: L cosθ L 3 cos(θ ) d cosθ 4 b = 0 L sinθ L 3 sin(θ ) d sinθ 4 + = 0 () Show the defined ngles on the digrm. (b) Write the velocit eqution. (c) Write the ccelertion eqution. () O L L 3 (3) d (4) b Problem. For this inverted slider-crnk mechnism, the necessr vectors for nlticl kinemtic nlsis re provided. () Construct the lgebric position equtions. (b) Identif the minimum number of vribles. (c) Show the defined ngles on the digrm. (d) Write the velocit eqution onl for the first position eqution (-component). (e) Write the ccelertion eqution ssocited with question (d). (f) Write epression for the coordintes of point Q. () L L 3 O Q (3) 45 o P d (4) P = L 4 PQ = L 5 b

3 Problem. For the mechnism shown, nswer the following questions. () Number of moving bodies: (b) Number of full joints: (c) Number of hlf joints: (d) Number of degrees of freedom bsed on the mobilit formul: Problem. For the mechnism shown the following constnt lengths re given: = 4.0, = 1.7, = 1.7 ) Construct vectors on the figure nd write the vector loop eqution. b) Show the ngle for ech vector. c) Construct the lgebric position equtions. d) Wht re the vribles in these equtions? Problem. For the mechnism shown, nswer the following questions. Number of moving bodies: Number of full joints: Number of hlf joints: Number of degrees of freedom bsed on the mobilit formul:

4 Problem. For four-br mechnism, the following link lengths re provided: = 5.0 (ground link), =.0 (crnk), = 7.0 (coupler), = 3.0 (follower). The ngle of the crnk is 10. () Drw the four-br in both of its configurtions (use n pproprite scle). (b) For the first configurtion wht re the ngles of the following vectors: R : R O4 : (c) For the second configurtion wht re the ngles of the following vectors: R : R O4 : Problem. For ech of the following four-br mechnism, determine the lengths of the links nd then use the formul to determine whether the mechnism is Grshof or not. Problem. For ech mechnism shown, nswer the following questions. Number of moving bodies: Number of full joints: Number of hlf joints: Number of degrees of freedom bsed on the mobilit formul: Number of degrees of freedom bsed on our intuition:

5 Problem. For this four-br mechnism the following constnt lengths re provided: = 8.5, =.0, = 7.3, = 5.3, D = 4.8, CD =.0 n nlticl kinemtic nlsis hs resulted in ngulr orienttions shown on the figure nd the following ngulr velocities nd ccelertions: ω = 1.5, ω 3 = 0., ω 4 = 0.6, α = 0.8, α 3 = 0.8, α 4 = 0. () Write vector epression for the coordinte, velocit nd ccelertion of point C. (b) Trnsform the vector epressions into lgebric C epressions. (Note tht the given ngles m not ectl represent the ngles for our position D vectors.) (c) Substitute the known quntities (for the constnts nd vribles) in the epressions. There is no 6 need to evlute the epressions. O