Page 175 - Dynamics of Mechanical Systems

0593_C05_fm Page 156 Monday, May 6, 2002 2:15 PM

156 Dynamics of Mechanical Systems

Problems

Section 5.2 Coordinates, Constraints, Degrees of Freedom
P5.2.1: Consider a pair of eyeglasses to be composed of a frame containing the lenses and
two rods hinged to the frame for fitting over the ears. How many degrees of freedom do
the eyeglasses have?
P5.2.2: Let a simple model of the human arm consist of three bodies representing the
upper arm, the lower arm, and the hands. Let the upper arm have a spherical (ball-and-
socket) connection with the chest, let the elbow be represented as a pin (or hinge), and
let the hand movement be governed by a twist of the lower arm and vertical and horizontal
rotations. How many degrees of freedom does the model have?
P5.2.3: How many degrees of freedom does a vice, as commonly found in a workshop,
have? (Include the axial rotation of the adjustment handle about its long axis and the
potential rotation of the vice itself about a vertical axis.)
P5.2.4: See Figure P5.2.4. A wheel W, having planar motion, rolls without slipping in a
straight line. Let C be the contact point between W and the rolling surface S. How many
degrees of freedom does W have? What are the constraint equations?

W

FIGURE P5.2.4 C S
A wheel rolling in a straight line.

P5.2.5: See Problem P5.2.4. Suppose W is allowed to slip along S. How many degrees of
freedom does W then have?
P5.2.6: How many degrees of freedom are there in a child’s tricycle whose wheels roll
without slipping on a flat horizontal surface? (Neglect the rotation of the pedals about
their individual axes.)

Section 5.3 Planar Motion of a Rigid Body
P5.3.1: Classify the movement of the following bodies as being (1) translation, (2) rotation,
and/or (3) general plane motion.

a. Eraser on a chalk board
b. Table-saw blade
c. Radial-arm-saw blade
d. Bicycle wheel of a bicycle moving in a straight line
e. Seat of a bicycle moving in a straight line
f. Foot pedal of a bicyclist moving in a straight line