Concept explainers
Roberts linkage is named after Richard Roberts (1789-1864) and can be used to draw a close approximation to a straight line by locating a pen at point F. The distance AB is the same as BF, DF, and DE. Knowing that at the instant shown bar AB has a constant angular velocity of 4 rad/s clockwise, determine (a) the angular acceleration of bar DE, (b) the acceleration of point F.
Fig. P 15.135
(a)
Angular acceleration of bar DE.
Answer to Problem 15.135P
The angular acceleration
Explanation of Solution
Given information:
Constant angular velocity of link AB is
The absolute value of point A:
The relative velocity of A with respect to B is defined as:
The absolute acceleration of point B is defined as:
The tangential acceleration is defined as:
The normal acceleration is defined as:
In above equations:
Calculation:
The position vector
The velocity
Substitute:
The position vector
The velocity
Substitute
For bar DE
The position vector
The velocity
Equate components in equation 1 and 2:
Therefore
Bar AB has constant angular velocity. Therefore angular acceleration
Acceleration
For object BDF:
Acceleration
Substitute:
For bar DE
Acceleration
Substitute
Equate components
Therefore
Conclusion:
The angular acceleration
(b)
Acceleration of point F.
Answer to Problem 15.135P
The acceleration
Explanation of Solution
Given information:
Constant angular velocity of link AB is
The absolute acceleration of point B is defined as:
The tangential acceleration is defined as:
The normal acceleration is defined as:
In above equations
Calculation:
According to sub part a:
The acceleration
Angular acceleration
Angular velocity
Position vector
Acceleration
Substitute
Solve
The magnitude and angle of acceleration
Conclusion:
The acceleration
Want to see more full solutions like this?
Chapter 15 Solutions
Vector Mechanics For Engineers
- 2) At the instant given, it is known that the angular velocity of rod AB is 20 rad/s clockwise. By use of Cartesian vector form, determine (a) the angular velocity of rod BD, (b) the velocity of the point D. 0.2 m 0.25 m D 0.2 m E -0.6 m Barrow_forwardQuestion 1. A linkage mechanism is shown in the figure below, where the Collar B moves downward to the left with a constant velocity of 1.6 m/s. At the instant shown when 0 40°, determine (a) the angular velocity of rod AB. (b) the velocity of collar A. B 60° 500 mmarrow_forwardProblem (8) The belt shown moves over two pulleys without slipping. At the instant shown the pulleys are rotating clockwise and the speed of point B on the belt is 4 m/s, increasing at the rate of 32 m/s?. Determine, at this instant, (a) the angular velocity and angular acceleration of each pulley, (b) the acceleration of point P on pulley C. B 160 mm fi00 mmarrow_forward
- A series of small machine components are moved by means of a conveyor belt that passes over a 6-in. idler pulley. radio. At the instant shown, point A's velocity is 13 in/s to the left and its acceleration is 5 in/s² to the right. Determine the angular velocity of the guide pulley. A 6 in. Barrow_forward2. In the position shown in Fig. 2, the angular velocity of bar O,A is a 2 rad/s. O,A-O,B-2 m, O,O₂-AB. Determine: Velocity and acceleration of point C of the triangle ABC. Fig. 2 noarrow_forwardRequired information NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. For a 5-m steel beam AE, the acceleration of point A is 2.5 m/s² downward and the angular acceleration of the beam is 1.5 rad/s2 counterclockwise. Knowing that at the instant considered the angular velocity of the beam is zero, determine the acceleration of cable B and cable D. A -1.5 m- B Determine the acceleration of cable B The acceleration of cable Bis 2 m 1.375 5 m/s2. D -1.5 m- Earrow_forward
- 1. Knowing that at the instant shown the velocity of collar A is 900 mm/s to the left, determine (a) the angular velocity of rod ADB, (b) the velocity of Point B. S0 mm 150 mm D 60 mm 120 mm B.arrow_forward0.2 m 0.25 m D E 0.6 m- Knowing that at the instant shown the angular velocity of rod AB is 15 rad/s clockwise, determine (a) the angular velocity of rod BD. (b) the velocity of the midpoint of rod BD. In the position shown, bar AB has an angular velocity of 4 rad/s clockwise. Determine the angular velocity of bars BD and DE. 200 mm 75 mm D 175 mm - 100 mm Earrow_forward15.125 Knowing that at the instant shown bar AB has a constant an- gular velocity of 19 rad/s clockwise, determine (a) the angular acceleration of bar BGD, (b) the angular acceleration of bar DE. 3.22.62 G 380 mm E A B 100 mm 0 200 mm 100 mm 100 mmarrow_forward
- The 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. 5 in. 10 in. C B -15 in.- -15 in.- Select one: O A. arm = 3 rad/s (CW); and @c = 1.5 rad/s (CW) O B. Warm = 5 rad/s (CW); and @c = 3 rad/s (CW) O C.o arm = 0 rad/s ; and @c = 1.5 rad/s (CCW) O D. warm = 1 rad/s (CW); and wc = 0 rad/sarrow_forwardi The mechanism shown below is made up of links OA and AB. Point O is pinned to ground i Point. B i constrained to move along a straight-line path. At the instant shown, link OA s ver- tical, link AB s horizontal. and vy is travelling at a constant speed of 5 m/s in the direction shown. ind: At this instant: ) The angular velocity of links OA and AB, 1) The angular acceleration of links OA and AB.arrow_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
- 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