All 16 Chapters Covered
SOLUTION MANUAL
, 1
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.
These 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 provided here.
1.2 The link lengths of a planar four-bar linkage are 1 in, 3 in, 5 in, and 5 in. 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 linkage or a drag-link linkage.
s =1 in, l = 5 in, p = 3 in, q = 5 in; these linkages all satisfy Grashof’s law
since1 in + 5 in 3 in + 5 in . Ans.
Drag-link linkage Drag-link linkage Ans.
Crank-rocker linkage Crank-rocker linkage Ans.
Double-rocker linkage Crank-rocker linkage Ans.
, 2
1.3 A crank-rocker linkage has a 100-mm frame, a 25-mm crank, a 90-mm coupler, and a 75-
mm rocker. Draw the linkage and find the maximum and minimum values of the
transmission angle. Locate both toggle postures and record the corresponding crank
angles and transmission angles.
Extremum transmission angles: min = 1 = 53.1 max = 3 = 98.1 Ans.
Toggle postures: 2 = 40.1 2 = 59.1 4 = 228.6 4 = 90.9 Ans.
1.4 Plot the complete path of coupler point C.
, 3
1.5 Find the mobility of each mechanism.
(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 the case of part (c); 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.
Note in part (d) that each pair of coaxial sliding ground joints is counted as only a
single prismatic pair.
SOLUTION MANUAL
, 1
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.
These 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 provided here.
1.2 The link lengths of a planar four-bar linkage are 1 in, 3 in, 5 in, and 5 in. 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 linkage or a drag-link linkage.
s =1 in, l = 5 in, p = 3 in, q = 5 in; these linkages all satisfy Grashof’s law
since1 in + 5 in 3 in + 5 in . Ans.
Drag-link linkage Drag-link linkage Ans.
Crank-rocker linkage Crank-rocker linkage Ans.
Double-rocker linkage Crank-rocker linkage Ans.
, 2
1.3 A crank-rocker linkage has a 100-mm frame, a 25-mm crank, a 90-mm coupler, and a 75-
mm rocker. Draw the linkage and find the maximum and minimum values of the
transmission angle. Locate both toggle postures and record the corresponding crank
angles and transmission angles.
Extremum transmission angles: min = 1 = 53.1 max = 3 = 98.1 Ans.
Toggle postures: 2 = 40.1 2 = 59.1 4 = 228.6 4 = 90.9 Ans.
1.4 Plot the complete path of coupler point C.
, 3
1.5 Find the mobility of each mechanism.
(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 the case of part (c); 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.
Note in part (d) that each pair of coaxial sliding ground joints is counted as only a
single prismatic pair.
