Solutions to Chapter 15 Exercise Problems
Problem 15.1
The figure below shows a system with two weights, WA and WB, which have been found to balance
a system of weights (not shown) on the shaft. The weights for W A and W B are 4 and 8 lb,
respectively, an

Kinematics and Dynamics of Machines of ENGR 3270U Lecture 1
Yuping He
University of Ontario Institute of Technology September 8, 2007
Course Instructor
Yuping He, PhD, PEng [email protected] Office: ENG 2023 Ext. 2783
Office hours: Tuesday 11:00 am 12:00

Solutions to Chapter 10 Exercise Problems
Problem 10.1
Two spur gears have a diametral pitch of 6. Gear 2 has 24 teeth, and gear 3 has 48. The working
pressure angle is 20, and both gears are standard involutes. Determine the length of the contact
line an

Solutions to Chapter 7 Exercise Problems
Problem 7.1 A coupler curve has the approximate straight-line section shown in the figure below. Design a four-bar linkage that will generate the portion of the curve shown. Describe the linkage in sufficient detai

Solutions to Chapter 6 Exercise Problems Problem 6.1: Design a double rocker, four-bar linkage so that the base link is 2-in and the output rocker is 1-in long. The input link turns counterclockwise 60 when the output link turns clockwise through 90. The

Solutions to Chapter 5 Exercise Problems
Problem 5.1 For the mechanism shown, do the following: a) Write the vector equation of the above linkage. b) Write the x and y displacement equations. c) Find the velocity component equations. d) Find the accelerat

Solutions to Chapter 11 Exercise Problems
Problem 11.1
Two helical gears are cut with a spur gear hob that has a diametral pitch of 4 and a pressure angle of
20. The pinion has 15 teeth, the gear has 35 teeth, and the helix angle is 30. Determine the mini

Solutions to Chapter 13 Exercise Problems
Problem 13.1
In the mechanism shown, sketch a free-body diagram of each link, and determine the force P that
is necessary for equilibrium if T 12=90 N-m and = 90.
B
E
C
3
T12
CD = 125 mm
AD = 60 mm
ED = 200 mm
EF

Solutions to Chapter 12 Exercise Problems
Problem 12.1
Find the angular velocity of gear 8 if the angular velocity of gear 2 is 800 rpm in the direction
shown.
3
7
5
15T
2
8
6
4
18T
25T
33T
44T
48T
18T
2
Solution:
The velocity ratio for the gear train is

Solutions to Chapter 14 Exercise Problems
Problem 14.1
The four-wheeled vehicle shown slides down a steep slope with its rear wheels locked (not
moving relative to the body) and its front wheels rolling freely. If M is the mass of the vehicle, h
the norma

Solutions to Chapter 9 Exercise Problems
Problem 9.1
For the information given, find the velocity of point C. Show all equations used with terms
properly labeled.
B
a
2
3
s
4
A
= 45, = 0.1 rad / s
= 90, = 0.1 rad / s
C
1
s = 2m, s = 0.5 m / s,
a = 2m
Solu

Solutions to Chapter 1 Exercise Problems
Problem 1.1 Find a mechanism as an isolated device or in a machine and make a realistic sketch of the mechanism. Then make a freehand sketch of the kinematic schematics for the mechanism chosen. Typical examples of

Solutions to Chapter 3 Exercise Problems Problem 3.1 In the figure below, points A and C have the same horizontal coordinate, and 3 = 30 rad/s. Draw and dimension the velocity polygon. Identify the sliding velocity between the block and the slide, and fin

Kinematics and Dynamics of Machines of ENGR 3270U Lecture 3
Yuping He
University of Ontario Institute of Technology September 15, 2008
1.5 Inversion
created by grounding a different link in a linkage to form various mechanisms all inversions of a particu

Kinematics and Dynamics of Machines of ENGR 3270U Lecture 4
Yuping He
University of Ontario Institute of Technology September 17, 2008
Chapter 2: Graphical Kinematic Chapter Analysis for Simple Mechanisms Analysis
2.1 Introduction
Approaches for planar li

Kinematics and Dynamics of Machines of ENGR 3270U Lecture 5
Yuping He
University of Ontario Institute of Technology September 22, 2008
Chapter 2: Graphical Kinematic Chapter Analysis for Simple Mechanisms Analysis
Example 1 Design a fourbar Grashof crank-

Kinematics and Dynamics of Machines of ENGR 3270U Lecture 6
Yuping He
University of Ontario Institute of Technology September 24, 2008
2.5 The Acceleration Image Theorem
Objective: To obtain accelerations of additional
points on a rigid body when the acce

Kinematics and Dynamics of Machines of ENGR 3270U Lecture 7
Yuping He
University of Ontario Institute of Technology October 6, 2008
Chapter 3 Linkages with Rolling and Sliding Contacts
3.1 Introduction
Position Analysis Position
y
Relative Motion
x
rB =

Solutions to Chapter 4 Exercise Problems Problem 4.1 Locate all of the instant centers in the mechanism shown below.
A 30 AB = 1.5" 2 63 B 3 1 4
Position Analysis Draw the linkage to scale. Start by locating point B. Then draw the line on which B must sli

Problem 2.21 Link 2 of the linkage shown in the figure has an angular velocity of 10 rad/s CCW. Find the angular velocity of link 6 and the velocities of points B, C, and D.
Y
C A 3 2 2 E 2 F 4 Position Analysis B 6 5 D
AE = 0.7" AB = 2.5" AC = 1.0" BC =

Solutions to Chapter 2 Exercise Problems Problem 2.1 In the mechanism shown below, link 2 is rotating CCW at the rate of 2 rad/s (constant). In the position shown, link 2 is horizontal and link 4 is vertical. Write the appropriate vector equations, solve

Kinematics and Dynamics of Machines of ENGR 3270U Lecture 2
Yuping He
University of Ontario Institute of Technology September 10, 2008
1.1 Planar Linkage (continued) 1.1 (continued)
Linkage = Links + Joints 1) Links binary ternary quaternary 2) Joints low