Theory of Machines and Mechanisms – Solutions Manual | Complete Worked Problems and Detailed Explanations

Solutions Manual to accompany

THEORY OF MACHINES
AND MECHANISMS
Fourth Edition International Version
PART 1


KINEMATICS AND MECHANISMS
Chapter 1


The World of Mechanisms
1.1 Sketch at least six different examples of the use of a planar four-bar linkage in practice.
They can be found in the workshop, in domestic appliances, on vehicles, on agricultural
machines, and so on.

Since the variety is unbounded no standard solutions are shown here.

1.2 The link lengths of a planar four-bar linkage are 0.2, 0.4, 0.6 and 0.6 m. Assemble the
links in all possible combinations and sketch the four inversions of each. Do these
linkages satisfy Grashof's law? Describe each inversion by name, for example, a crank-
rocker mechanism or a drag-link mechanism.
s  0.2, l  0.6, p  0.4, q  0.6 ; these linkages all satisfy Grashof’s law
since 0.2  0.6  0.4  0.6 . Ans.




Drag-link mechanism Drag-link mechanism Ans.

, Crank-rocker mechanism Crank-rocker mechanism Ans.




Double-rocker mechanism Crank-rocker mechanism Ans.
1.3 A crank-rocker linkage has a 250 mm frame, a 62.5 mm crank, a 225 mm coupler, and a
187.5 mm rocker. Draw the linkage and find the maximum and minimum values of the
transmission angle. Locate both toggle positions and record the corresponding crank
angles and transmission angles.

, Extremum transmission angles:  min   1  53.1  max   3  98.1 Ans.
Toggle positions:   40.1   59.1   228.6   90.9 Ans.

1.4 In Fig. P1.4, point C is attached to the coupler; plot its complete path.




1.5 Find the mobility of each mechanism illustrated in Fig. P1.5.

, (a) n  6, j1  7, j2  0; m  36 1  27 10  1 Ans.
(b) n  8, j1  10, j2  0; m  38 1  210 10 1 Ans.
(c) n  7, j1  9, j2  0; m  37 1  29 10  0 Ans.
Note that the Kutzbach criterion fails in this case; the true mobility is m=1. The
exception is due to a redundant constraint. The assumption that the rolling contact
joint does not allow links 2 and 3 to separate duplicates the constraint of the fixed
link length O2O3 .
(d) n  4, j1  3, j2  2; m  34 1  23 12  1 Ans.
Notice that each coaxial pair of sliding ground joints is counted as only a single
prismatic pair.

1.6 Use the Kutzbach criterion to determine the mobility of the mechanism illustrated in Fig.
P1.6.




n  5, j1  5, j2 1; m  35 1  25 11  1 Ans.
Notice that the double pin is counted as two single j1 pins.

1.7 Find a planar mechanism with a mobility of one that contains a moving quaternary link.