Index 159
double chain with non-intersecting
element 40, 46–48
general double chain linkage 48
double-Hooke’s-joint linkage 18, 24, 26, 33,
154
duel quaternion 10, 12
eccentricity 75, 76
equilibrium matrix 34
Escrig, F. 62, 155, 157
Evans, J. 136, 155
even number 47, 48
expandable structure 41
expanded configuration 62, 73, 99, 106, 127
expansion sequence 36, 52, 53, 55, 59, 60,
73, 74, 144, 150
flat profile 85, 86, 112
folding chair 62
four-bar linkage, 9, 12, 17, 18, 21
four-bar spherical linkage 10
fixed point 9, 52–57
fixed reference frame 5, 11–13
folded configuration 97, 102, 107, 126, 130,
134
Fontené 40
full cycle mobility 35
Gantes, C. 62, 156
gear 1, 8, 9, 18
geometry 15, 17, 34
Goldberg, M. 21, 22, 156
Goldberg linkage 21–27, 154–157
Goldberg 5R linkage 21–25, 33
Goldberg 6R linkage 22–24, 33
Goldberg L-shaped 6R linkage 24
generalised Goldberg 5R linkages, 24
syncopated Goldberg 5R linkage 22, 23
syncopated Goldberg 6R linkage 24, 25
syncopated Goldberg L-shaped 6R linkage
24
ground 5, 7, 9, 12
Grübler–Kutzbach mobility criterion see
Kutzbach criterion
Grünbaum, B. 136, 137, 151, 156
Guideline 81–83, 88, 91, 92, 112, 144
Hartenberg, R. S. 10, 14, 20, 155, 156
Hedgepeth, J. M. 102, 155
heptagon 18
hexagonal prism 112, 114
hinge 5, 37, 41, 111
Hoberman, C. 38, 52, 156
Hoberman sphere 1, 36, 39
homogeneous coordinate 14
Hu, M. 21, 94, 154
Hunt, K. H. 6, 156
independent coordinates 4
infinitesimal 35
inflatable structure 1
input 4, 7, 12
input–output curve 118, 119, 124, 128, 129
intermediate tie 65, 66, 71, 73
isosceles triangle 66, 67, 90
Jensen, F. 61, 156
joint see kinematic joint
kaleidocycle 31, 32, 154, 157
Kempe, A. B. 40, 156
Kempe linkage 40, 41, 154
kinematic chain 4, 15, 18
kinematic joint 4–6
ball joint 5
cylindrical joint 5
cylindrical roller 6
higher pair 4, 6
lower pair 4, 5, 8
planar joint 5
prismatic joint 5, 8
revolute joint 5, 8
screw joint 5
spatial point contact 5
spherical joint 5
kinematic variable 15, 33
kinematically indeterminate 35
kinematics 4, 10
Kuipers, J. 10, 156
Kutzbach criterion 6, 7, 9, 17, 34, 41
layout 52, 69, 77, 111, 136–152
lazy tong 38
Lee, C.-C. 18, 156
length 11, 12, 14, 16, 19, 20, 22, 35, 47, 56,
57, 65–69, 71, 72, 75–77, 78, 81, 82, 84,
88, 90, 92, 94, 96, 100–102, 119, 122,
126, 130, 132
Lie algebra 10
Lie group 10
link 4
linkage 1, 2, 4, 6
planar linkage 2, 8, 15
spatial linkage 2, 6
spherical linkage 9
overconstrained linkage 17–33, 35, 62,
117, 151
Liu, S. Y. 146, 156
locked chain 5
loop parallelogram constraint 43–49, 52,
153
Luo, Y. 61, 156
Mao, D. 41, 156
matrix method 10, 12–15, 20, 133
Mavroidis, C. 25, 156
maximum coverage 99
Maxwell’s rule 33, 34, 154
McCarthy, J. M. 10, 156
mechanism 1–6, 33–35
overconstrained mechanism, 17, 18, 151,
152
planar mechanism 8, 11, 15, 77
spherical mechanism 8, 9, 16
three dimensional mechanism 8, 77
Meurant, R. 62, 156
mobile assembly 88, 92, 94, 111, 119, 122,
138, 150
mobility 4, 6–9, 15, 17, 33, 35
most compact folding 96
double chain with non-intersecting
element 40, 46–48
general double chain linkage 48
double-Hooke’s-joint linkage 18, 24, 26, 33,
154
duel quaternion 10, 12
eccentricity 75, 76
equilibrium matrix 34
Escrig, F. 62, 155, 157
Evans, J. 136, 155
even number 47, 48
expandable structure 41
expanded configuration 62, 73, 99, 106, 127
expansion sequence 36, 52, 53, 55, 59, 60,
73, 74, 144, 150
flat profile 85, 86, 112
folding chair 62
four-bar linkage, 9, 12, 17, 18, 21
four-bar spherical linkage 10
fixed point 9, 52–57
fixed reference frame 5, 11–13
folded configuration 97, 102, 107, 126, 130,
134
Fontené 40
full cycle mobility 35
Gantes, C. 62, 156
gear 1, 8, 9, 18
geometry 15, 17, 34
Goldberg, M. 21, 22, 156
Goldberg linkage 21–27, 154–157
Goldberg 5R linkage 21–25, 33
Goldberg 6R linkage 22–24, 33
Goldberg L-shaped 6R linkage 24
generalised Goldberg 5R linkages, 24
syncopated Goldberg 5R linkage 22, 23
syncopated Goldberg 6R linkage 24, 25
syncopated Goldberg L-shaped 6R linkage
24
ground 5, 7, 9, 12
Grübler–Kutzbach mobility criterion see
Kutzbach criterion
Grünbaum, B. 136, 137, 151, 156
Guideline 81–83, 88, 91, 92, 112, 144
Hartenberg, R. S. 10, 14, 20, 155, 156
Hedgepeth, J. M. 102, 155
heptagon 18
hexagonal prism 112, 114
hinge 5, 37, 41, 111
Hoberman, C. 38, 52, 156
Hoberman sphere 1, 36, 39
homogeneous coordinate 14
Hu, M. 21, 94, 154
Hunt, K. H. 6, 156
independent coordinates 4
infinitesimal 35
inflatable structure 1
input 4, 7, 12
input–output curve 118, 119, 124, 128, 129
intermediate tie 65, 66, 71, 73
isosceles triangle 66, 67, 90
Jensen, F. 61, 156
joint see kinematic joint
kaleidocycle 31, 32, 154, 157
Kempe, A. B. 40, 156
Kempe linkage 40, 41, 154
kinematic chain 4, 15, 18
kinematic joint 4–6
ball joint 5
cylindrical joint 5
cylindrical roller 6
higher pair 4, 6
lower pair 4, 5, 8
planar joint 5
prismatic joint 5, 8
revolute joint 5, 8
screw joint 5
spatial point contact 5
spherical joint 5
kinematic variable 15, 33
kinematically indeterminate 35
kinematics 4, 10
Kuipers, J. 10, 156
Kutzbach criterion 6, 7, 9, 17, 34, 41
layout 52, 69, 77, 111, 136–152
lazy tong 38
Lee, C.-C. 18, 156
length 11, 12, 14, 16, 19, 20, 22, 35, 47, 56,
57, 65–69, 71, 72, 75–77, 78, 81, 82, 84,
88, 90, 92, 94, 96, 100–102, 119, 122,
126, 130, 132
Lie algebra 10
Lie group 10
link 4
linkage 1, 2, 4, 6
planar linkage 2, 8, 15
spatial linkage 2, 6
spherical linkage 9
overconstrained linkage 17–33, 35, 62,
117, 151
Liu, S. Y. 146, 156
locked chain 5
loop parallelogram constraint 43–49, 52,
153
Luo, Y. 61, 156
Mao, D. 41, 156
matrix method 10, 12–15, 20, 133
Mavroidis, C. 25, 156
maximum coverage 99
Maxwell’s rule 33, 34, 154
McCarthy, J. M. 10, 156
mechanism 1–6, 33–35
overconstrained mechanism, 17, 18, 151,
152
planar mechanism 8, 11, 15, 77
spherical mechanism 8, 9, 16
three dimensional mechanism 8, 77
Meurant, R. 62, 156
mobile assembly 88, 92, 94, 111, 119, 122,
138, 150
mobility 4, 6–9, 15, 17, 33, 35
most compact folding 96