Concept explainers
The arm ABC rotates with an angular velocity of 4 rad/s counterclockwise. Knowing that the angular velocity of the intermediate gear B is 8 rad/s counterclockwise, determine (a) the instantaneous centers of rotation of gears A and C, (b) the angular velocities of gears A and C.
Fig. P15.80
(a)
Find the instantaneous center of rotation of gear A and C.
Answer to Problem 15.80P
The instantaneous center of rotation of the gear A is
The instantaneous center of rotation of the gear C is
Explanation of Solution
Given information:
The angular velocity of the arm ABC is
The angular velocity of the gear B is
Consider the contact point between the gear A and B is denoted by 1.
Consider the contact point between the gear B and C is denoted by 2.
Consider the velocity at point A, C, 1, and 2 are denoted by
Calculation:
Show the velocity at point A and C as shown in Figure 1.
Refer to Figure 1.
Consider the arm ABC.
Calculate the velocity at A and C as follows:
Take the value of
Show the gear B as shown in Figure 2.
Refer Figure 2.
Calculate the velocity at point 1 and 2 as follows:
Take the angular velocity of the gear B is
Show the gear A as shown in Figure 3.
Refer Figure 3.
Consider the instantaneous center of rotation of the gear A is denoted by
Calculate the angular acceleration
Substitute
Calculate the distance
Substitute
Thus, the instantaneous center of rotation of the gear A is
Show the gear C as shown in Figure 4.
Refer Figure 4.
Consider the instantaneous center of rotation of the gear C is denoted by
Calculate the angular acceleration
Substitute
Calculate the distance
Substitute
Thus, the instantaneous center of rotation of the gear C is
(b)
Find the angular velocity of gear A and C.
Answer to Problem 15.80P
The angular velocity of the gear A and C are
Explanation of Solution
Given information:
Calculation:
Refer Part (a).
Refer Equation (1).
The angular velocity of the gear A is
Refer Equation (2).
The angular velocity of the gear C is
Thus, the angular velocity of the gear A and C are
Want to see more full solutions like this?
Chapter 15 Solutions
Connect 2 Semester Access Card for Vector Mechanics for Engineers: Statics and Dynamics
- Knowing that at the instant shown the angular velocity of bar AB is 15 rad/s clockwise and the angular velocity of bar EF is 10 rad/s clockwise, determine (a) the angular velocity of rod DE, (b) the relative velocity of collar B with respect to rod DE.arrow_forwardIn a four-link mechanism, the dimensions of the links are given as AB=50mm, BC=66mm, CD=56mm, and AD=100mm. At the instant when <DAB = 60° , the link AB has an angular velocity of 10.5 rad/sec in the counterclockwise direction. Both A and D lies in the horizontal plane.For the given configuration of the mechanism, determine the following: angular velocity of the link CD, angular velocity of the link BC, velocity of an offset point G on the link CD if CG=24mm,DG=44mm Instructions: configuration diagram Scale: 1:1 velocity diagram. Scale: 1m/s : 95mmarrow_forwardKnowing that the angular velocity of rod DE is a constant 20 rad/s clockwise, determine in the position shown (a) the angular velocity of rod BD, (b) the velocity of the midpoint of rod BD. Solve using instantaneous center. The answer for WBD should be -5 rad/s and for Vc is 1.63 m/s. ] Please show every step on a piece of paper, if typed sometimes it gets cut off.arrow_forward
- In a four bar mechanism, the dimensions of the links are as given below:AB = 50 mm, BC = 66 mmCD = 56 mm and AD = 100 mmAt a given instant when | DAB=60°the angular velocity of link AB is 10.5rad/sec in CCW direction.Determine,i) Velocity of point Cii) Velocity of point E on link BC when BE = 40 mmiii) The angular velocity of link BC and CDiv) The velocity of an offset point F on link BC, if BF = 45 mm,CF = 30 mm and BCF is read clockwise.v) The velocity of an offset point G on link CD, if CG = 24mm, DG = 44 mm and DCG is read clockwise.vi) The velocity of rubbing of pins A, B, C and D. The ratios ofthe pins are 30 mm, 40 mm, 25 mm and 35 mmrespectively.arrow_forwardThe outer gear A rotates with an angular velocity of 6 rad/s counterclockwise. Knowing that the angular velocity of the intermediate gear B is 3 rad/s clockwise, determine: 1. The angular velocity of the arm ABC 2. The angular velocity of the outer gear C. Select one: A. ωarm=3 ω a r m = 3 rad/s (CW); and ωC=1.5 ω C = 1.5 rad/s (CW) B. ωarm=5 ω a r m = 5 rad/s (CW); and ωC=3 ω C = 3 rad/s (CW) C. ωarm=0 ω a r m = 0 rad/s ; and ωC=1.5 ω C = 1.5 rad/s (CCW) D. ωarm=1 ω a r m = 1 rad/s (CW); and ωC=0 ω C = 0 rad/sarrow_forwardThe bar AB of 3.62kg is attached to the collar A of negligible mass and a wheel of mass 15.81kg with a turning radius of 0.16m. If at the position shown the angular velocity of the wheel is 67rpm clockwise, determine the velocity of the wheel in RPM when point B is located just below C. The angle of the bar with respect to Y is 19.47°. The answer is 93.89arrow_forward
- 15.8 The gears A, B, and C, of radii rA=500 mm, rB=200 mm, rC=150 mm, respectively, all rotate around fixed axes parallel to the x-axis shown. At a certain instance, gear A rotates with wA=6i rad/s and gear C rotates with aC=10 rad/s2. Determine wB and aB at this instant.arrow_forward15.27 The crank OA of a slider-crank mechanism rotates with a constant angular velocity of 3.6 rad/s clockwise. Determine wAB of the connecting rod AB and vB of the slider B when (a) theta=90 degrees, (b) theta=180 degrees.arrow_forwardA painter is half way up a 10-m ladder when the bottom starts sliding out from under him. Knowing that point A has a velocity vA = 2 m/s directed to the left when 0= 60°, determine (a) the angular velocity of the ladder, (b) the velocity of the painter.arrow_forward
- Problem 1: In a four bar mechanism, the dimensions of the links are as given below: AB = 50 mm, BC = 66 mm CD = 56 mm and AD = 100 mm At a given instant when |DAB 60o the angular velocity of link AB is 10.5 r/s in CCW direction. Determine, i) Velocity of point C ii) Velocity of point E on link BC when BE = 40 mm iii) The angular velocity of link BC and CD iv) The velocity of an offset point F on link BC, if BF = 45 mm, CF = 30 mm and BCF is read clockwise. v) The velocity of an offset point G on link CD, if CG = 24 mm, DG = 44 mm and DCG is read clockwise. vi) The velocity of rubbing of pins A, B, C and D. The ratio of the pins are 30 mm, 40 mm, 25 mm and 35 mm respectively.arrow_forwardIn a four bar mechanism, the dimensions of the links are given as AB = 50 mm, BC = 66 mm, CD = 56 mm and AD = 100 mm. At a given instant when <DAB=600 . The angular velocity of link AB is 10.5r/s in CCW direction. Determine, (i) velocity of point C, (ii) velocity of point E on link BC when BE = 40 mm, (iii) the angular velocity of link BC and CD; (iv) the velocity of an offset point F on link BC, if BF = 45 mm, CF = 30 mm and BCF is read clockwise. (v) the velocity of an offset point G on link CD, if CG = 24 mm, DG = 44 mm and DCG is read clockwise (arrow_forwardThe arm that joins gears A and B rotates anti-clockwise with 24 rad/s. At the same time, gear A rotates at 4.8 rad/s also anti-clockwise, determine by IC the angular velocity of gear B and speed VBarrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY