Chapter 1 Practice Problems

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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.

(Introduction to Mechanism Design with Computer Applications, 1e Eric Constans) (Solution Manual all Chapters) 1 / 4

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Problem 1.3 How many degrees of freedom do the following joints on your body permit?

• Your knee
• Your ankle
• Your shoulder
• Your hip
• A knuckle on one of your fingers

Solution

a. 1 – Your knee can only rotate in one direction. Hint: Kicking a ball.

• 3 – Your ankle can flex up and down, slightly from side to side, as well as rotate.
• 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.

• 3 – Your hip can move your body and legs up and down, side to side, and rotate your

legs.

• 2 – Your knuckles can move up and down and side to side, however, you cannot

rotate your finger.

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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.

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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 ���=3(�−1)−2(� �+� ��)−� ℎ�

=3(5−1)−2(6)

=0 This linkage is a structure.

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