Kinematics of Machines Homework Help

PROBLEM 3 (30 points)Due to slipping, points A and B on the rim of the disk have the velocities shown. Determine the velocity of point D at this instant.1. Using the relative equation 2. Using the IC method

The 3-lb block A is hanging in the stationary position shown when it is hit by the 5-oz ball B. If the velocity of ball B just before it hits block A is 40 ft/s as shown, determine the velocity of ball B and the velocity of block A immediately after the impact (Specify the direction of the results). Assuming the coefficient of restitution between A and B is e = 0,7. Determine the maximum angle 0that block A swings through.

A sketch of a front loader is shown in Figure 1. a. Draw a kinematic diagram of the mechanism. b. Specify the number of links, the number and the type of joints,and calculate the mobility for the mechanism

Consider the step-down (buck) dc-dc converter shown in the figure below, in which all components are ideal. Assume the output voltage Vo = 5 V, held constant by controlling the duty cycle D = ton/T; the PWM control responds to the output voltage feedback by adjusting the switch "on time" ton to that fraction of the switching period T required to hold the output constant.The switching frequency is set at 50 kHz. The input voltage Vin varies from 10 V to 40 V.Calculate the minimum inductance L required to keep the converter operation in a continuous-conduction mode under all conditions (Vin= 10 V to 40 V). [Select the one best answer from the choices given below.]

PROBLEM 1 (30 points)Determine the angular velocity of link CD if link AB has the angular velocity shown. 1. Use the relative equation 2. Use the IC method

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5. (10 points) Calculate the mobility using the Kutzbach criterion. Clearly number each link and label the lower pairs (j,) and higher pairs (j,) on the diagram. Comment on whether the calculated mobility makes sense. # of binary links: # of ternary links: # of quaternary links: i, joints: jz joints: Consider the vehicle body and wheels to be stationary, as part of the fixed ground.

2- Problem 5.8: . A 1130-kg car is held in place by a light cable on a very smooth(frictionless) ramp, as shown in Fig. E5.8. The cable makes an angle of 31.0° above thesurface of the ramp, and the ramp itself rises at 25.0° above the horizontal. (a) Draw afree-body diagram for the car. (b) Find the tension in the cable. (c) How hard does thesurface of the ramp push on the car?ble

3. ACCELERATION: A four-bar linkage is shown below. Find the magnitude and direction of a, and a. (B) (5 points) Find the magnitude and direction of the absolute acceleration ofpoint E on link 3. RAD= 10 cm, RBp = 15 cm, RBc = 60 cm; RCE = 65 cm; RĘF = 15 cm(Note: ADB and FEC are right triangles.) w2 = 2 rad/s cw az = 1 rad/s? ccw A velocity analysis has already been completed. resulting in these values: W3 = 0.449 rad/s ccw Wa = 0.462 rad/s cw%D

4. VELOCITY DIFFERENCES. A toy boat is moving in a pool with the velocity indicated below. An ant, A,is on the corner of a rotating square plate, which pivots about a fixed point in the pool. The plate is85 cm on each side and is rotating 0.5 rad/s ccw. In this problem, you will report the boat's observationof how fast the ant appears to be moving (i.e. the apparent velocity). (A) (8 points) Assume the ant has not yet started walking. Determine and draw the velocity vector ofthe ant as observed by the boat, VAB: Report the magnitude and direction of this vector. (B) (8 points) Assume the ant starts walking straight along the edge, with the velocity indicated below.Building off of part (A), determine and draw the velocity vector of the ant as observed by the boat, V,(This can easily be done on the same diagram from part (A).) Report the magnitude and direction ofthis vector.AB.

6. (A) (6 points) Airline overhead bin mechanism. Calculate the mobility using the Kutzbach criterion. Clearly number each link and label the lower pairs (j,) and higher pairs (j2) on the diagram. Consider the vehicle body and wheels to be stationary, as part of the fixed ground. # of binary links: # of ternary links: # of quaternary links: j, joints: J2 joints: (B) (6 points) Calculate the Grash of Condition and report whether any of the links can achieve continuous rotation.

Determine the reaction forces in all kinematic pairs and the torque M; for 2 necessary to balance external forces F., Fs and torqueM3

A10.1 – Continuation of A8.2. The inversion of a slider-crank mechanism shown below is driven by link 2 atw2 = 20 rad/s ccw. Using the velocity data found in A8.2, find the angular accelerations of links 3 and 4.Also find the linear acceleration vectors for point C and point P, both located on link 3. Report both magnitude and direction for all quantities. RBA = 40 mm RCA = 35 mm RBp = 142 mm ZCAB = 75°

A10.2 Continuation of A9.3. ACCELERATION DIFFERENCES. A toy boat is moving in a pool with the velocity and acceleration indicated below. An ant is on the corner of a rotating square plate, which pivots about a fixed point in the pool. The plate is 55 cm on each side and is rotating 0.5 rad/s ccw. The plate is also accelerating at 1 rad/s² ccw. In this problem, you will report the boat's observation of how fast the ant appears to be accelerating. (A) Assume the ant has not yet started walking. Determine and draw the acceleration difference vector of the ant with respect to the boat, Ap4B2. Report the magnitude and direction of this vector. (B) Assume the ant has been walking straight along the edge, with the velocity and acceleration indicated below. Building off of part (A), determine and draw the acceleration difference vector of the ant with respect to boat, A'D4B2: (This can easily be done on the same diagram from part (A).) Report the magnitude and direction of this vector.

Problem 6.30 in the text Engineering Dynamics by Ginsberg. While you may think that you require the mass of the bar, that is not the case. When you set up the equations of motion,you will be able to solve for the two normal forces and the quantity mo in terms of the applied load (mg). You can then solve for o by dividing both sides by m. (Granted, if you wanted to get the normal forces, you would need the mass of the bar.) Answer: o-22.45 rad.(Not the answer in the back of the book.)sec2-

2/117 The shafts and attached brackets are twisted in opposite directions to maintain a tension T of 500 N in the wire joining A and B. Express the tension,considered as a force acting on A, as a vector in the form of Eq. 2/12 and determine the projection of Tonto the line DC. F = F(li + mj + nk) Where l=\cos \theta_{x} m=\cos \theta_{y} n=\cos \theta_{z} Equation 2/12:

12-85. The flight path of the helicopter as it takes off from A is defined by the parametric equations x = (2²) m and y= (0.04) m, where t is the time in seconds. Determine the distance the helicopter is from point A and the magnitudes of its velocity and acceleration when t=10 s.

12-23. A particle is moving along a straight line such that its acceleration is defined as a – ( 2u) m/s², where v is in meters per second. If v – 20 m/s when s – 0 and t – 0, determine the particle's position, velocity, and acceleration as functions of time.