Find: Determine the velocity and acceleration of end P. Write your answers as vectors.

Transcription

1 Homework 2. Given: ar P rotates about a shaft passing through end of the bar. t the instant shown, the angular velocity and angular acceleration of P are given by ω and α. atics Homework Problems ME 274 II-11 (5/12) Find: Determine the velocity and acceleration of end P. Write your answers as vectors. tates about a shaft passing d of the bar. t the instant e angular velocity and angular n of P are given by! and!. the velocity and acceleration of ite your answers as vectors. y rotation of bar P h b Use the following parameters in your analysis: ω = 2 rad/s (CCW), α = 3 rad/s 2 (CW), b = 500 rad / sec ( CCWmm), and! = h 3 = rad 200 / sec mm. 2 ( CW ), b = 500 mm and h = 200 mm in sis. Freeform c

2 Homework 2. Given: The rectangular plate CD freely rotates about a pivot at point. t the instant shown, the acceleration of point C is given by a C = a î + a y ĵ. Find: Determine the angular velocity ω and angular acceleration α of the plate. y C 0.25 m 0.5 m D Use the following parameters in your analysis: a = 0 and a y = -20 m/s 2. 2 Freeform c 2016

3 Planar Kinematics Homework Problems ME 274 Homework 2.C Problem II-5 Given: The wheel shown below rolls without slip on cart. The cart has velocity v = v î and acceleration The wheel a = shown a î. The below center rolls ofwithout the wheel slip has on velocity cart. v ssuming C = v C î and that acceleration the cart has a C velocity = a C î. v = v i and acceleration a = a i, and the center of the wheel has velocity v C = v C i Find: Determine the velocity and acceleration of point. and acceleration a C = a C i, determine the velocity and acceleration of point. r C y a Use the following parameters in your analysis: r = 0.5 m, v = 5 m/s, v C = -10 m/s, a = -8 m/s 2 and a C = -6 m/s 2. Use the following: r = 2 ft, v = 10 ft / sec, v C =!5 ft / sec, a =!10 ft / sec 2 and a C =!6 ft / sec 2. Freeform c

4 Planar Kinematics Homework Problems ME 274 Homework 2.D Given: Problem The sliding II-9 collar moves horizontally along the shaft producing an oscillation in. t the instant shown, and C are horizontal and vertical, respectively, and the velocity of C is not changing The sliding (v C is collar constant) moves ashorizontally C moves to the along right. the shaft producing an oscillation in. If, at the instant shown, and C are horizontal and vertical, respectively, and the velocity Find: of Determine C is not thechanging angular acceleration ( v C = constant of. ) as C moves to the right, find the angular acceleration of. r L C v C Use the following: L = 0.6 m, r = 0.8 m and v C = 25 m / sec. Use the following parameters in your analysis: L = 2 ft, r = 1.5 ft and v C = 40 ft/s. 4 Freeform c 2016

5 atics Homework Problems ME 274 II-20 ism is made up Homework of links, 2.E D and DE. t the instant shown, links and rtical, and link D is horizontal. For this position: Given: mechanism is made up of links, D and DE. t the instant shown, links and termine the angular DE are velocities vertical, of and links link D and is horizontal. D. Write your answers as ctors. termine the angular Find: accelerations For this position: of links and D. Write your answers as ctors. (a) Determine the angular velocities of links and D. Write your answers as vectors. ft and! DE = (b) 2 rad Determine / sec = constant the angular in your accelerations analysis. of links and D. Write your answers as vectors. E! DE 2L 2L L D Use the following parameters in your analysis: L = 3 ft and ω DE = 3 rad/s = constant. Freeform c

6 Homework 2.F Planar Kinematics Homework Problems ME 274 Problem Given: II-23 mechanism is made up of links and D, with point being pinned to ground and point being a pin joint connecting links and D. slider is connected to D at pin D with mechanism the slider being is made constrained up of links to move and ond, a circular with point path with being a radius pinned of to R. ground t the and position shown point below, being linka pin isjoint vertical, connecting link Dlinks is horizontal and D. and Dslider is directly is connected above point to D. at t pin this position, D with D isthe traveling slider being to theconstrained right with ato constant move on speed a circular of v D path. with a radius of 2.5 meters. t the position shown below, link is vertical, link D is horizontal and D is directly above Find: point For. this t this position: position, D is traveling to the right with a constant speed of 5 m/sec. For the position shown, find: (a) Determine the angular velocities of links and D. Write your answers as vectors. i) the angular velocity of links and D, and ii) (b) the Determine angular acceleration the angular accelerations of links and of links D. and D. Write your answers as vectors. y d D v D L R Use the following parameters in your analysis: R = 0.5 m, L = 2 m, d = 1.5 m and v D = 5 m/s. 6 Freeform c 2016

7 ar Kinematics Homework Problems ME 274 blem II-19 Homework 2.G echanism is made Given: up of links mechanism, D isand made DE. upt ofthe links instant, shown, D andlinks DE. t the and instant shown, links and are aligned horizontally, D are aligned and link horizontally, DE is vertical. and link For DE this isposition: vertical. a) locate the instant center for link D. Find: For this position: b) determine the angular velocities of links D and DE. Write your answers as vectors. (a) Locate the instant center for link D. (b) Determine the angular velocities of links D and DE. Write your answers as vectors. L = 1 ft and! = "4 rad / sec in your analysis. E 2L! L 2L D Use the following parameters in your analysis: L = 1 ft and ω = 8 rad/s. Freeform c

8 Homework 2.H Consider the four mechanisms shown below. Respond to the questions posed. Feel free to draw directly on these sheets and submit for your homework solution. Use a straight edge when making your drawings. MECHNISM N. 1 Link is rotating in the clockwise sense. Determine the location of the instant center (IC) of link. From the location of this IC, determine the sense of rotation for links and C. Justify your answers in words. C 8 Freeform c 2016

9 MECHNISM N. 2 Determine the location of the instant center (IC) of link D. From the location of this IC, determine the sense of rotation for links D and D. Justify your answers in words. C D v Freeform c

10 MECHNISM N. 3 Link is rotating in the clockwise sense. Determine the location of the instant center (IC) of link. From the location of this IC, determine the sense of rotation for link and the sense of translation for the piston. Justify your answers in words. 10 Freeform c 2016

11 MECHNISM N. 4 Racks and are moving in the directions shown with the speeds provided. ssume that the gear does not slip on the racks. Determine the location of the instant center (IC) of the gear. From the location of this IC, determine the sense of rotation for the gear. Justify your answers with numbers and words. v = 0.3 m/s 0.1 m 0.2 m v = 0.1 m/s Freeform c

12 Homework 3. Given: Particle P moves within a straight slot cut into a rotating disk with the -position of P increasing at a constant rate of ẋ. The disk is rotating with counter-clockwise sense at a speed of Ω, changing at a rate of Ω. The yz coordinate system is attached to the disk with its origin at the center of the disk. Frame Kinematics Homework Problems ME 274 Find: For this problem: (a) Determine the velocity and acceleration of particle P. Epress your answers as vectors in terms of their -y components. oves within a straight slot cut into a rotating disk with the -position of P constant rate of (b)! Make. The adisk sketch is rotating of the velocity with counter-clockwise and accelerationsense vectors at a found above. ith! changing at a rate of!. The yz coordinate system is attached to ts origin at the center of the disk. ine the velocity and acceleration of y e P. Epress your answers as vectors in f their -y components.! sketch of the velocity and acceleration found in a) above. h P ing parameters Use in your the following analysis: parameters = 0.8 ft, inh your = 0.6analysis: ft,! = 15 = ft 1.5 / s, ft, h = 0.6 ft, ẋ = -10 ft/s, Ω = 6 rad/s and Ω = -4 and!! = "5 rad / s 2 rad/s Freeform c 2016

13 Homework 3. Given: n L-shaped arm E is pinned to ground at (section is perpendicular to section rence Frame Kinematics E of Homework E). Problems rm E is known to be rotating in the counterclockwise ME 274 sense with a constant rotational speed of Ω. Rigid link P is pinned to ground at, and with P able to slide within a slot that is cut into section E of arm E, as shown. The yz coordinate system is attached to III-3 arm E with its origin at pin. For the position shown, section is aligned with the direction ped arm E is of pinned, and to Pground is at aat position (section of y P within is perpendicular the slot. to section E). rm E is known to be rotating in the counterclockwise sense with a rotational speed Find: of!. For Rigid this link position: P is pinned to ground at, and with P able to in a slot that is cut into section E of arm E, as shown. The yz coordinate attached to arm (a) E Determine with its the origin angular at pin velocity. of link P. Write your answer as a vector. (b) Determine the angular acceleration of link P. Write your answer as a vector. osition shown, section is aligned with the direction of, and P is at a f y P within the slot. For this E etermine the angular locity of link P. Write y P ur answer as a vector. etermine the angular celeration of link P. Write ur answer as a vector. y P L! b Use the following parameters in your analysis: Ω = 4 rad/s, y P = 2 ft, L = 5 ft and b = 3 ft. ollowing parameters in your analysis:! = 2 rad / sec, y P = 2 ft, L = 2.5 ft ft. Freeform c