Husty,
M.
,
Pfurner,
M.
,
Schröcker,
H.-P.
, and
Brunnthaler,
K.
, 2007, “
Algebraic Methods in Mechanism Analysis and Synthesis,” Robotica,
25(6), pp. 661–675.

[CrossRef]
Gogu,
G.
, 2008, “
Constraint Singularities and the Structural Parameters of Parallel Robots,” Advances in Robot Kinematics: Analysis and Design,
J. Lenarcic and
P. Wenger
, eds.,
Springer,
Amsterdam.

Dai,
J.
,
Huang,
Z.
, and
Lipkin,
H.
, 2006, “
Mobility of Overconstrained Parallel Mechanisms,” ASME J. Mech. Des.,
128(1), pp. 220–229.

[CrossRef]
Zhao,
J.-S.
,
Feng,
Z.-J.
, and
Dong,
J.-X.
, 2006, “
Computation of the Configuration Degree of Freedom of a Spatial Parallel Mechanism by Using Reciprocal Screw Theory,” Mech. Mach. Theory,
41(12), pp. 1486–1504.

[CrossRef]
Kong,
X.
, and
Gosselin,
C. M.
, 2007, Type Synthesis of Parallel Mechanisms,
Springer, Berlin.

Baker,
J. E.
, 1980, “
An Analysis of the Bricard Linkages,” Mech. Mach. Theory,
15(4), pp. 267–286.

[CrossRef]
Waldron,
K. J.
, 1973, “
A Study of Overconstrained Linkage Geometry by Solution of Closure Equations—Part II. Four-Bar Linkages With Lower Pairs Other Than Screw Joints,” Mech. Mach. Theory,
8(2), pp. 233–247.

[CrossRef]
Mavroidis,
C.
, and
Roth,
B.
, 1995, “
Analysis of Overconstrained Mechanisms,” ASME J. Mech. Des.,
117(1), pp. 69–74.

[CrossRef]
Gogu,
G.
, 2005, “
Mobility and Spatiality of Parallel Robots Revisited Via the Theory of Linear Transformations,” Eur. J. Mech. A/Solids,
24(4), pp. 690–711.

[CrossRef]
Kong,
X.
, 2014, “
Reconfiguration Analysis of a 3-DOF Parallel Mechanism Using Euler Parameter Quaternions and Algebraic Geometry Method,” Mech. Mach. Theory,
74, pp. 188–201.

[CrossRef]
Kong,
X.
, and
Pfurner,
M.
, 2015, “
Type Synthesis and Reconfiguration Analysis of a Class of Variable-DOF Single-Loop Mechanisms,” Mech. Mach. Theory,
85, pp. 116–128.

[CrossRef]
Arponen,
T.
,
Piipponen,
S.
, and
Tuomela,
J.
, 2009, “
Kinematic Analysis of Bricard's Mechanism,” Nonlinear Dyn.,
56(1), pp. 85–99.

[CrossRef]
Arponen,
T.
,
Müller,
A.
,
Piipponen,
S.
, and
Tuomela,
J.
, 2014, “
Kinematical Analysis of Overconstrained and Underconstrained Mechanisms by Means of Computational Algebraic Geometry,” Meccanica,
49(4), pp. 843–862.

[CrossRef]
Liu,
R.
,
Serré,
P.
, and
Rameau,
J. F.
, 2013, “
A Tool to Check Mobility Under Parameter Variations in Over-Constrained Mechanisms,” Mech. Mach. Theory,
69, pp. 44–61.

[CrossRef]
Wampler,
C. W.
, and
Sommese,
A. J.
, 2011, “
Numerical Algebraic Geometry and Kinematics,” Acta Numer.,
20, pp. 469–567.

[CrossRef]
Wampler,
C. W.
,
Hauenstein,
J. D.
, and
Sommese,
A. J.
, 2011, “
Mechanism Mobility and a Local Dimension Test,” Mech. Mach. Theory,
46(9), pp. 1193–1206.

[CrossRef]
Rico,
J. M.
,
Gallardo,
J.
, and
Duffy,
J.
, 1999, “
Screw Theory and Higher Order Kinematic Analysis of Open Serial and Closed Chains,” Mech. Mach. Theory,
34(4), pp. 559–586.

[CrossRef]
Gallardo-Alvarado,
J.
, and
Rico-Martinez,
J. M.
, 2001, “
Jerk Influence Coefficients, Via Screw Theory, of Closed Chains,” Meccanica,
36(2), pp. 213–228.

[CrossRef]
Cervantes-Sánchez,
J. J.
,
Rico-Martínez,
J. M.
,
González-Montiel,
G.
, and
González-Galván,
E. J.
, 2009, “
The Differential Calculus of Screws: Theory, Geometrical Interpretation, and Applications,” Proc. Inst. Mech. E., Part C: J. Mech. Eng. Sci.,
223(6), pp. 1449–1468.

[CrossRef]
Müller,
A.
, 2002, “
Higher Order Local Analysis of Singularities in Parallel Mechanisms,” ASME Paper No. DETC2002/MECH-34258.

Müller,
A.
, 2014, “
Higher Derivatives of the Kinematic Mapping and Some Applications,” Mech. Mach. Theory,
76, pp. 70–85.

[CrossRef]
Müller,
A.
, “
Higher-Order Constraints for Linkages With Lower Kinematic Pairs,” Mech. Mach. Theory,
100, pp. 33–43.

Lerbet,
J.
, 1999, “
Analytic Geometry and Singularities of Mechanisms,” Z. Angew. Math. Mech.,
78(10b), pp. 687–694.

Whitney,
H.
, 1965, “Local Properties of Analytic Varieties, Differential and Combinatorial Topology,” A Symposium in Honor of Marston Morse (Princeton Mathematical Series 27), S. S. Cairns, ed.,
Princeton University Press, Princeton, NJ.

Müller,
A.
, and
Rico,
J. M.
, 2008, “
Mobility and Higher Order Local Analysis of the Configuration Space of Single-Loop Mechanisms,” Advances in Robot Kinematics,
J. J. Lenarcic and
P. Wenger
, eds.,
Springer, Amsterdam, pp. 215–224.

Chen,
C.
, 2011, “
The Order of Local Mobility of Mechanisms,” Mech. Mach. Theory,
46(9), pp. 1251–1264.

[CrossRef]
de Bustos,
I. F.
,
Aguirrebeitia,
J.
,
Avilés,
R.
, and
Ansola,
R.
, 2012, “
Second Order Mobility Analysis of Mechanisms Using Closure Equations,” Meccanica,
47(7), pp. 1695–1704.

[CrossRef]
Karger,
A.
, 1996, “
Singularity Analysis of Serial Robot-Manipulators,” ASME J. Mech. Des.,
118(4), pp. 520–525.

[CrossRef]
Wohlhart,
K.
, 1999, “
Degrees of Shakiness,” Mech. Mach. Theory,
34(7), pp. 1103–1126.

[CrossRef]
Connelly,
R.
, and
Servatius,
H.
, 1994, “
Higher-Order Rigidity–What is the Proper Definition?,” Discrete Comput. Geom.,
11(2), pp. 193–200.

[CrossRef]
Wohlhart,
K.
, 2010, “
From Higher Degrees of Shakiness to Mobility,” Mech. Mach. Theory,
45(3), pp. 467–476.

[CrossRef]
Müller,
A.
, 2015, “
Representation of the Kinematic Topology of Mechanisms for Kinematic Analysis,” Mech. Sci.,
6, pp. 1–10.

[CrossRef]
Müller,
A.
, 2015, “
Local Analysis of Closed-Loop Linkages: Mobility, Singularities, and Shakiness,” ASME Paper No. DETC2015-47485.

Chai,
W. H.
, and
Chen,
Y.
, “
The Line-Symmetric Octahedral Bricard Linkage and Its Structural Closure,” Mech. Mach. Theory,
45(5), pp. 772–779.

[CrossRef]
Wohlhart,
K.
, 1996, “
Kinematotropic Linkages,” Recent Advances in Robot Kinematics,
J. Lenarčič and
V. Parent-Castelli
, eds.,
Kluwer, Alphen aan den Rijn, The Netherlands, pp. 359–368.

Golubitsky,
M.
, and
Guillemin,
V.
, 1973, Stable Mappings and Their Singularities,
Springer,
New York.

Zlatanov,
D.
,
Bonev,
I. A.
, and
Gosselin,
C. M.
, 2002, “
Constraint Singularities as C-Space Singularities,” 8th International Symposium on Advances in Robot Kinematics (ARK 2002), Caldes de Malavella, Spain, June 24–28.

Kutznetsov,
E. N.
, 1991, “
Systems With Infinitesimal Mobility—Part I: Matrix Analysis and First-Order Infinitesimal Mobility,” ASME J. Appl. Mech.,
58(2), pp. 513–526.

[CrossRef]
Brockett,
R. W.
, 1984, “
Robotic Manipulators and the Product of Exponentials Formula, Mathematical Theory of Networks and Systems,” Lect. Notes Control Inf. Sci.,
58, pp. 120–129.

Selig,
J.
, 2005, Geometric Fundamentals of Robotics, Monographs in Computer Science Series,
Springer-Verlag,
New York.

Müller,
A.
, 2014, “
Derivatives of Screw Systems in Body-Fixed Representation,” Advances in Robot Kinematics (ARK),
J. Lenarcic and
O. Khatib
, eds.,
Springer, Cham, Switzerland, pp. 123–130.

Rameau,
J. F.
, and
Serré,
P.
, 2015, “
Computing Mobility Condition Using Groebner Basis,” Mech. Mach. Theory,
91, pp. 21–38.

[CrossRef]
Greuel,
G. M.
, and
Pfister,
G.
, 2012, A Singular Introduction to Commutative Algebra,
Springer, Berlin.

Cox,
D.
,
Little,
J.
, and
O'Shea,
D.
, 2007, Ideals, Varieties and Algorithms, 3rd ed.,
Springer,
Berlin.

Goldberg,
M
, 1943, “
New Five-Bar and Six-Bar Linkages in Three Dimensions,” Trans. ASME,
65, pp. 649–661.

Baker,
J. E.
, 1993, “
A Comparative Survey of the Bennett-Based, 6-Revolute Kinematic Loops,” Mech. Mach. Theory,
28(1), pp. 83–96.

[CrossRef]
Servatius,
B.
,
Shai,
O.
, and
Whiteley,
W.
, 2010, “
Geometric Properties of Assur Graphs,” Eur. J. Combinatorics,
31(4), pp. 1105–1120.

[CrossRef]