(Introduction to Mechanism Design with Computer Applications, 1e Eric Constans)
(Solution Manual all Chapters)
Chapter 1 Practice Problems
Problem 1.1
What is the definition of a rigid body? Describe types of motion that a rigid body can experience.
Solution
A rigid body is any two points separated by some distance, and maintain that distance throughout
any motion. Rigid bodies can experience several types of motion, the first being a simple rotation
in which all points on the body can describe a circular arc of constant radius about a single point,
or the center of rotation. The second being a translation, in which all points on the body describe
a straight line parallel to all other points on the body. Lastly is complex motion, this occurs when
the rigid body is exposed to a combination of translation and rotation.
Problem 1.2
Define the term Degrees of Freedom. What does it mean if a linkage has a negative Degree of
Freedom?
Solution
Degrees of Freedom are a number of independent coordinates to completely define an objects
position in free space. Having a negative number for Degrees of Freedom means that such an
object is preloaded, or the object cannot be created because it would require the links to bend,
using rigid links the structure cannot be created. Thus demonstrating a negative Degree of
Freedom; a preloaded structure.
1
,Problem 1.3
How many degrees of freedom do the following joints on your body permit?
a. Your knee
b. Your ankle
c. Your shoulder
d. Your hip
e. A knuckle on one of your fingers
Solution
a. 1 – Your knee can only rotate in one direction. Hint: Kicking a ball.
b. 3 – Your ankle can flex up and down, slightly from side to side, as well as rotate.
c. 3 – You can move your shoulder in all three positions. Hint: You can lift your arm up
and down, front to back, and make a big circle.
d. 3 – Your hip can move your body and legs up and down, side to side, and rotate your
legs.
e. 2 – Your knuckles can move up and down and side to side, however, you cannot
rotate your finger.
2
, Figure 1: Problem 1.4
Problem 1.4
Figure 1 shows a simple roller bearing. How many degrees of freedom does the roller bearing
have if the outer race is fixed to ground? Sketch the bearing, and indicate an appropriate set of
coordinates that completely specify the configuration of the bearing.
3
, Figure 2: Problem 1.5
Problem 1.5
How many degrees of freedom does the linkage in the Figure 2 have? Is it a mechanism, a
structure, or a preloaded structure?
Solution
𝐷𝑂𝐹 = 3(𝐿 − 1) − 2(𝐽𝑝 + 𝐽𝑓𝑠 ) − 𝐽ℎ𝑠
= 3(5 − 1) − 2(6)
=0
This linkage is a structure.
4
(Solution Manual all Chapters)
Chapter 1 Practice Problems
Problem 1.1
What is the definition of a rigid body? Describe types of motion that a rigid body can experience.
Solution
A rigid body is any two points separated by some distance, and maintain that distance throughout
any motion. Rigid bodies can experience several types of motion, the first being a simple rotation
in which all points on the body can describe a circular arc of constant radius about a single point,
or the center of rotation. The second being a translation, in which all points on the body describe
a straight line parallel to all other points on the body. Lastly is complex motion, this occurs when
the rigid body is exposed to a combination of translation and rotation.
Problem 1.2
Define the term Degrees of Freedom. What does it mean if a linkage has a negative Degree of
Freedom?
Solution
Degrees of Freedom are a number of independent coordinates to completely define an objects
position in free space. Having a negative number for Degrees of Freedom means that such an
object is preloaded, or the object cannot be created because it would require the links to bend,
using rigid links the structure cannot be created. Thus demonstrating a negative Degree of
Freedom; a preloaded structure.
1
,Problem 1.3
How many degrees of freedom do the following joints on your body permit?
a. Your knee
b. Your ankle
c. Your shoulder
d. Your hip
e. A knuckle on one of your fingers
Solution
a. 1 – Your knee can only rotate in one direction. Hint: Kicking a ball.
b. 3 – Your ankle can flex up and down, slightly from side to side, as well as rotate.
c. 3 – You can move your shoulder in all three positions. Hint: You can lift your arm up
and down, front to back, and make a big circle.
d. 3 – Your hip can move your body and legs up and down, side to side, and rotate your
legs.
e. 2 – Your knuckles can move up and down and side to side, however, you cannot
rotate your finger.
2
, Figure 1: Problem 1.4
Problem 1.4
Figure 1 shows a simple roller bearing. How many degrees of freedom does the roller bearing
have if the outer race is fixed to ground? Sketch the bearing, and indicate an appropriate set of
coordinates that completely specify the configuration of the bearing.
3
, Figure 2: Problem 1.5
Problem 1.5
How many degrees of freedom does the linkage in the Figure 2 have? Is it a mechanism, a
structure, or a preloaded structure?
Solution
𝐷𝑂𝐹 = 3(𝐿 − 1) − 2(𝐽𝑝 + 𝐽𝑓𝑠 ) − 𝐽ℎ𝑠
= 3(5 − 1) − 2(6)
=0
This linkage is a structure.
4
