DESIGN OF MACHINERY
6th Edition
ISBN: 9781260113310
Author: Norton
Publisher: RENT MCG
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Chapter 3, Problem 3.45P
To determine
To prove:the true relationships of angular velocities of links in the Roberts diagram given in Figure 3-25.
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3.9 The linkage in Fig. 3-10 has 0,A = 8mm, AB = 19. 3mm, AC = 13. 3mm, and offset =
%3D
3. 8mm. The crank angle in the position shown is 34. 3° and ZBAC =38. 6°. Find wz, vA, VB, Vc
for the position shown for w, = 15rad/s in the direction shown. ( Choose two methods)
1) Use the velocity difference graphical method.
2) Use the instantaneous center graphical method.
3) Use the analytical method.
@2
B
offset
02
Fig. 3-10
Problem 4: For the following mechanism, (a) Find all instant centers (
(b) Find the mechanical advantage (MA) of the mechanism
Drawing is to-scale.
TMM
1
Fin
2
MM
THIM
1
Fout
Write about the motions which are required to form a kinematic pair with suitable
examples.
Chapter 3 Solutions
DESIGN OF MACHINERY
Ch. 3 - Define the following examples as path, motion, or...Ch. 3 - Design a fourbar Grashof crank-rocker for 90 of...Ch. 3 - Prob. 3.3PCh. 3 - Design a fourbar mechanism to give the two...Ch. 3 - Prob. 3.5PCh. 3 - Prob. 3.6PCh. 3 - Repeat Problem 3-2 with a quick-return time ratio...Ch. 3 - Design a sixbar drag link quick-return linkage for...Ch. 3 - Design a crank-shaper quick-return mechanism for a...Ch. 3 - Find the two cognates of the linkage in Figure...
Ch. 3 - Find the three equivalent geared fivebar linkages...Ch. 3 - Design a sixbar single-dwell linkage for a dwell...Ch. 3 - Design a sixbar double-dwell linkage for a dwell...Ch. 3 - Figure P3-3 shows a treadle-operated grinding...Ch. 3 - Figure P3-4 shows a non-Grashof fourbar linkage...Ch. 3 - Prob. 3.16PCh. 3 - Prob. 3.17PCh. 3 - Prob. 3.18PCh. 3 - Design a pin-jointed linkage that will guide the...Ch. 3 - Figure P3-6 shows a V-link off-loading mechanism...Ch. 3 - Prob. 3.21PCh. 3 - Prob. 3.22PCh. 3 - Figure P3-8 shows a fourbar linkage used in a...Ch. 3 - Prob. 3.24PCh. 3 - Prob. 3.25PCh. 3 - Prob. 3.26PCh. 3 - Prob. 3.27PCh. 3 - Prob. 3.28PCh. 3 - Prob. 3.29PCh. 3 - Prob. 3.30PCh. 3 - Design a Hoeken straight-line linkage to give...Ch. 3 - Design a Hoeken straight-line linkage to give...Ch. 3 - Prob. 3.33PCh. 3 - Prob. 3.34PCh. 3 - Prob. 3.35PCh. 3 - Find the Grashof condition, inversion, any limit...Ch. 3 - Prob. 3.37PCh. 3 - Prob. 3.38PCh. 3 - Prob. 3.39PCh. 3 - Draw the Roberts diagram and find the cognates of...Ch. 3 - Prob. 3.41PCh. 3 - Find the Grashof condition, any limit positions,...Ch. 3 - Prob. 3.43PCh. 3 - Prob. 3.44PCh. 3 - Prob. 3.45PCh. 3 - Prob. 3.46PCh. 3 - Prob. 3.47PCh. 3 - Prob. 3.48PCh. 3 - Prob. 3.49PCh. 3 - Prob. 3.50PCh. 3 - Prob. 3.51PCh. 3 - Prob. 3.52PCh. 3 - Prob. 3.53PCh. 3 - Prob. 3.54PCh. 3 - Prob. 3.55PCh. 3 - Prob. 3.56PCh. 3 - Prob. 3.57PCh. 3 - Prob. 3.58PCh. 3 - Prob. 3.59PCh. 3 - Prob. 3.60PCh. 3 - Prob. 3.61PCh. 3 - Prob. 3.62PCh. 3 - Prob. 3.63PCh. 3 - Prob. 3.64PCh. 3 - Prob. 3.65PCh. 3 - Prob. 3.66PCh. 3 - Design a fourbar Grashof crank-rocker for 120 of...Ch. 3 - Prob. 3.68PCh. 3 - Design a fourbar Grashof crank-rocker for 80 of...Ch. 3 - Design a sixbar drag link quick-return linkage for...Ch. 3 - Design a crank shaper quick-return mechanism for a...Ch. 3 - Design a sixbar, single-dwell linkage for a dwell...Ch. 3 - Design a sixbar, single-dwell linkage for a dwell...Ch. 3 - Prob. 3.74PCh. 3 - Using the method of Example 3-11, show that the...Ch. 3 - Prob. 3.76PCh. 3 - Prob. 3.77PCh. 3 - Prob. 3.78PCh. 3 - The first set of 10 coupler curves on page 1 of...Ch. 3 - Prob. 3.80PCh. 3 - Prob. 3.81PCh. 3 - Prob. 3.82PCh. 3 - Prob. 3.83PCh. 3 - Prob. 3.84PCh. 3 - Prob. 3.85PCh. 3 - Prob. 3.86PCh. 3 - Prob. 3.87PCh. 3 - The side view of the upper section of a...Ch. 3 - Design a fourbar mechanism to give the three...Ch. 3 - Design a fourbar mechanism to give the three...Ch. 3 - Design a fourbar Grashof crank-rocker for 60...Ch. 3 - Design a crank-shaper quick-return mechanism for a...Ch. 3 - Figure P3-22 shows a non-Grashof fourbar linkage...Ch. 3 - Prob. 3.94PCh. 3 - Design a fourbar Grashof crank-rocker for 80...Ch. 3 - Design a sixbar drag link quick-return linkage for...
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- A general inverted fourbar slider-crank linkage has links length: link 2 = a = 2, link 4 = c = 4, and link 1= d = 6 in. The input values are 02 = 60°, y = 90°. The linkage configuration and terminology are shown in figure below; note that this figure does not represent the real dimensions of the linkage We need to find the angular positions of link 4 (04), of link 3 (03) and the effective length of link 3 (b) for both open and crossed configurations. 03 Өд В 4 RB 02 02 1 02 04 Choose... For open configuration, the angle 04 measured form X axis CCW in degree = Choose... For open configuration, the angle 03 measured form X axis CCW in degree = Choose... + For open configuration, the absolute value of the effective length of link 3, b = Choose... For crossed configuration, the angle 04 measured form X axis CCW in degree = Choose... For crossed configuration, the angle 03 measured form X axis CCW in degree = Choose... For crossed configuration, the absolute value of the effective length of…arrow_forwardB (2 28 -26- 20.4 D 5.2 Angular Displacement by Graphical Position Analysis Graphically position the links for the mechanism shown in the figure as Link 2, which is initially inclined 80° to the horizontal, is rotated 90° counter clockwise. Determine the angular displacement of Link 4 in degrees.arrow_forwardDraw the kinematic diagram of the given mechanism below. Calculate its mobility as well in terms of the number of degrees offreedom. In addition to this, determine and locate all instant centers of the given mechanism on the kinematic diagram that will becreated.arrow_forward
- 6) For the system shown, assume x-y-z is the inertial frame. If the bar first twists around A about the z-axis by a-70°, then the bar BD spins by 0-30° (shown in the picture). Define the transformation matrix to the Bar frame (B) from the Inertia frame (I) and find the location of C with respect to point O expressed in the inertial frame. (Assume a=0 as shown in the picture). 2 ft r=1 ft. B @=30⁰ 1.5 ftarrow_forwardOestion-1: An elliptical trammel is a double slider-crank mechanism used for drawing ellipses as shown in figure (a) below. Position vectors for various linkages are drawn as shown in figure (b). Where: R2: represents position vector for a Slider which can slide along x-axis only R4: represents position vector for a Slider which can slide along y-axis only R3 represents position vector for a crank (Take R3 = 10mm, 03 = 45°, V3 = 10mm/sec) Rix: This is aligned with x-axis and represents fixed position of slider (R4) from ground RIY: This is aligned with Y-axis and represents fixed position of slider (R2) from ground Take: R13= 20mm, Rịy=40mm. Assume crank is rotating with constant velocity Note: all angles are measured counterclockwise from x-axis. a) Formulate the vector loop, position, velocity and acceleration equations b) Simplify the equations by plugging in respective angles and solve to find R2, R4, linear velocities of both sliders and angular acceleration of crank. c) Identify…arrow_forwardA general pinjointed fourbar linkage is shown in the figure below. It has the followings: The link lengths are L1 = 8.50 in., L2 = 3.00 in., L3 = 5.00 in. and L4 = 4.50 in. The values of θ1 = 0, θ2 = 60°, and θ4 = 119°. The angular velocity of link2 ω2 = 10 rad/s CCW. The angular velocities of link 3 ω3 and and link 4 ω4 are: Select one: a. ω3 = 5.29 rad/s CW, ω4 = 4.80 rad/s CCW b. ω3 = 5.29rad/s CW, ω4 = 6.14 rad/s CW c. ω3 = 3.94 rad/s CCW, ω4 = 4.8 rad/s CCW d. ω3 = 3.94 rad/s CCW, ω4 = 6.14 rad/s CCWarrow_forward
- Determine the degree of freedom of the mechanism in the figure below. Then determine all the centers of the era. Then use it to find the angular velocity of link 4 as well as the sliding velocity, knowing w_2 = 10 rad /s clockwise. Note that you must specify the order and method of determining non-obvious centers. %3D PE 4 5 D. C B Link radius 2:-25mm Link radius 5:-10mm BD length: -55 and DE length=30mm its angle with a horizon of 45 degrees and also the radius of curvature of the earth at point F is equal to 20 mm. The segment AB is horizontal and BD is vertical. The contact at point Cis of the rolling type with slip and at point F the rolling is pure. 2.arrow_forwardtheta O = 55 The link length and value of O2 for some four bar linkage are defined below, (drive link =4.2 cm , coupler link =5.9 cm , follower link = 5.9 cm, fixed link= 6.85 cm 1. draw the linkage to scale and graphically find all possible solution (both open and cross) for 03 and O4 2. If w = 2 rad /s (CCW) find the angular velocity for bar 3 and 4 3.if a= 5 rad/s? (Ccw) find the normal and tangential acceleration for link 3 and 4arrow_forwardQestion-1: A slider-crank mechanism is shown in figure below. Position vectors for various linkages are drawn as shown in figure. Length of the rotating Link-1 (L1) is continuously changing due to the slider placed on it. Link-3 is fixed and aligned along y-axis. Note: All angles are measured anti-clockwise from x-axis and Link-1 is rotating with uniform velocity Take: L2 = 20mm, 02 =45°, L3= 30mm, o=10rad/sec, V2= 1000mm/s. a) Formulate the vector loop, position, velocity and acceleration equations b) Solve to find 01, L1, linear velocity of slider and angular acceleration of link-1. c) Identify if the mechanism can be declared as spatial or planar mechanism also identify total number of full and half joints.arrow_forward
- Problem 4.7 ( example on analytical position analysis of pinjointed fourbar linkage) The link lengths and the value of 0, for some fourbar linkages are defined in Table P4-1. 1. For row a, find all possible solutions (both open and crossed) for angles 0, and 0, using the vector loop method. R3 R4 R2 R1 04 FIGURE 4-6arrow_forwardProblem 4-9a The link lengths and offset (a, b, c) and the value of 02 for an offset crank-slider linkage are defined as 1.4 in, 4 in, 1 in, 45°, respectively. Draw the scaled linkage and graphically find all possible solutions (both open and crossed) for angle 0z and slide position d. - slider axis B R3 A R4 offset R, 04 02 (This is not the scaled kinematic diagram.) Problem 4-10a Repeat Problem 4-9a except solve by the vector loop method.arrow_forwardA general pinjointed fourbar linkage is shown in the figure below. It has the followings: The link lengths are L1 = 8.50 in., L2 = 3.00 in., L3 = 5.00 in. and L4 = 4.50 in. The values of e1 = 0, 02 = 60°, and 04 = 119°. The angular velocity of link2 w2 = 10 rad/s CCW. L4 2 = 60° Ao B. O, = 0° Figure 5.32 Problems 5.3 and 5.4 The angular velocities of link 3 wz and and link 4 wa are: Select one: O a. w3 = 5.29rad/s CW, w4 = 6.14 rad/s CW O b. w3 = 3.94 rad/s CCW, W4 = 4.8 rad/s CCW O c. W3 = 3.94 rad/s CCW, wa = 6.14 rad/s CCW %3D O d. w3 = 5.29 rad/s CW, w4 = 4.80 rad/s CCW %3D %3Darrow_forward
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