Tangential intersection of branches of motion

Kinematic geometry of mechanisms

Hunt, K. H. (1978) · Medical Entomology and Zoology · Cited by 1,917

Singularity analysis of closed-loop kinematic chains

Gosselin, C., & Angeles, J. (1990) · IEEE Transactions on Robotics and Automation · doi:10.1109/70.56660 · Cited by 1,752

Mobility in Metamorphic Mechanisms of Foldable/Erectable Kinds

Dai, J. S., & Jones, J. R. (1999) · Journal of Mechanical Design · doi:10.1115/1.2829470 · Cited by 577

Tangents to an Analytic Variety

Whitney, H. (1965) · Annals of Mathematics · doi:10.2307/1970400 · Cited by 382

Tangents to an Analytic Variety

Whitney, H. (1992) · Birkhäuser Boston eBooks · doi:10.1007/978-1-4612-2972-8_34 · Cited by 351

Singularity Analysis of Closed Kinematic Chains

Park, F. C., & Kim, J. W. (1999) · Journal of Mechanical Design · doi:10.1115/1.2829426 · Cited by 234

Type Synthesis of Parallel Mechanisms With Multiple Operation Modes

Kong, X., Gosselin, C., & Richard, P.-L. (2006) · Journal of Mechanical Design · doi:10.1115/1.2717228 · Cited by 196

Recent Advances in Robot Kinematics

(1996) · Springer eBooks · doi:10.1007/978-94-009-1718-7 · Cited by 182

Single-loop kinematotropic mechanisms

Galletti, C., & Fanghella, P. (2001) · Mechanism and Machine Theory · doi:10.1016/s0094-114x(01)00002-7 · Cited by 175

Kinematotropic Linkages

Wohlhart, K. (1996) · Springer eBooks · doi:10.1007/978-94-009-1718-7_36 · Cited by 174

Mobility Change in Two Types of Metamorphic Parallel Mechanisms

Gan, D., Dai, J. S., & Liao, Q. (2009) · Journal of Mechanisms and Robotics · doi:10.1115/1.3211023 · Cited by 163

An analysis of the Bricard linkages

Baker, J. E. (1980) · Mechanism and Machine Theory · doi:10.1016/0094-114x(80)90021-x · Cited by 156

Parallel Mechanisms With Bifurcation of Schoenflies Motion

Li, Q., & Hervé, J. M. (2009) · IEEE Transactions on Robotics · doi:10.1109/tro.2008.2008737 · Cited by 141

Screw theory and higher order kinematic analysis of open serial and closed chains

Rico, J. M., Gallardo-Alvarado, J., & Duffy, J. (1999) · Mechanism and Machine Theory · doi:10.1016/s0094-114x(98)00029-9 · Cited by 137

Algebraic methods in mechanism analysis and synthesis

Husty, M. L., Pfurner, M., Schröcker, H.-P., & Brunnthaler, K. (2007) · Robotica · doi:10.1017/s0263574707003530 · Cited by 134

Topology and Constraint Analysis of Phase Change in the Metamorphic Chain and Its Evolved Mechanism

Zhang, K., Dai, J. S., & Fang, Y. (2010) · Journal of Mechanical Design · doi:10.1115/1.4002691 · Cited by 130

Constraint analysis on mobility change of a novel metamorphic parallel mechanism

Gan, D., Dai, J. S., & Liao, Q. (2010) · Mechanism and Machine Theory · doi:10.1016/j.mechmachtheory.2010.08.004 · Cited by 128

Reconfiguration analysis of a 3-DOF parallel mechanism using Euler parameter quaternions and algebraic geometry method

Kong, X. (2014) · Mechanism and Machine Theory · doi:10.1016/j.mechmachtheory.2013.12.010 · Cited by 113

Advances in Robot Kinematics

Altafini, C. (2005) · Automatica · doi:10.1016/j.automatica.2005.05.010 · Cited by 113

Systematization of morphing in reconfigurable mechanisms

Aimedee, F., Gogu, G., Dai, J. S., Bouzgarrou, C., & Bouton, N. (2015) · Mechanism and Machine Theory · doi:10.1016/j.mechmachtheory.2015.07.009 · Cited by 105

Leçons de cinématique

Bricard, R. (1926) · Virtual Defense Library (Ministerio de Defensa) · Cited by 98

Type synthesis and reconfiguration analysis of a class of variable-DOF single-loop mechanisms

Kong, X., & Pfurner, M. (2014) · Mechanism and Machine Theory · doi:10.1016/j.mechmachtheory.2014.10.011 · Cited by 95

Biological Modeling and Evolution Based Synthesis of Metamorphic Mechanisms

Zhang, L., Wang, D., & Dai, J. S. (2008) · Journal of Mechanical Design · doi:10.1115/1.2900719 · Cited by 94

Advances in Reconfigurable Mechanisms and Robots II

Ding, X., Kong, X., & Dai, J. S. (2015) · Mechanisms and machine science · doi:10.1007/978-3-319-23327-7 · Cited by 89

Parallel robots that change their group of motion

Fanghella, P., Galletti, C., & Giannotti, E. (2006) · Springer eBooks · doi:10.1007/978-1-4020-4941-5_6 · Cited by 86

Screw-System-Variation Enabled Reconfiguration of the Bennett Plano-Spherical Hybrid Linkage and Its Evolved Parallel Mechanism

Zhang, K., & Dai, J. S. (2015) · Journal of Mechanical Design · doi:10.1115/1.4030015 · Cited by 81

Multi-furcation in a derivative queer-square mechanism

Qin, Y., Dai, J. S., & Gogu, G. (2014) · Mechanism and Machine Theory · doi:10.1016/j.mechmachtheory.2014.06.006 · Cited by 77

Reconfigurability and unified kinematics modeling of a 3rTPS metamorphic parallel mechanism with perpendicular constraint screws

Gan, D., Dai, J. S., Dias, J. M. M., & Seneviratne, L. D. (2013) · Robotics and Computer-Integrated Manufacturing · doi:10.1016/j.rcim.2012.11.006 · Cited by 74

Computational Kinematics

Kecskeméthy, A., & Müller, A. (2009) · Springer eBooks · doi:10.1007/978-3-642-01947-0 · Cited by 74

Generic mobility of rigid body mechanisms

Müller, A. (2008) · Mechanism and Machine Theory · doi:10.1016/j.mechmachtheory.2008.08.002 · Cited by 71

Reconfiguration of Spatial Metamorphic Mechanisms

Zhang, L., & Dai, J. S. (2008) · Journal of Mechanisms and Robotics · doi:10.1115/1.2963025 · Cited by 69

Reconfiguration-aimed and manifold-operation based type synthesis of metamorphic parallel mechanisms with motion between 1R2T and 2R1T

Wei, J., & Dai, J. S. (2019) · Mechanism and Machine Theory · doi:10.1016/j.mechmachtheory.2019.04.001 · Cited by 69

Advances in robot kinematics: Analysis and control

(1999) · Computers & Mathematics with Applications · doi:10.1016/s0898-1221(99)90195-5 · Cited by 68

Advances in Robot Kinematics

Gregorio, R. D., & V., P. (2002) · Springer eBooks · doi:10.1007/978-94-017-0657-5 · Cited by 67

Higher-order rigidity—What is the proper definition?

Connelly, R., & Servatius, H. (1994) · Discrete & Computational Geometry · doi:10.1007/bf02574003 · Cited by 66

Local Kinematic Analysis of Closed-Loop Linkages—Mobility, Singularities, and Shakiness

Müller, A. (2016) · Journal of Mechanisms and Robotics · doi:10.1115/1.4032778 · Cited by 63

A complete kinematic analysis of the SNU 3-UPU parallel robot

Walter, D. R., Husty, M. L., & Pfurner, M. (2009) · Contemporary mathematics - American Mathematical Society · doi:10.1090/conm/496/09732 · Cited by 61

A 6R linkage reconfigurable between the line-symmetric Bricard linkage and the Bennett linkage

Song, C., Chen, Y., & Chen, I. (2013) · Mechanism and Machine Theory · doi:10.1016/j.mechmachtheory.2013.07.013 · Cited by 60

An overview of formulae for the higher-order kinematics of lower-pair chains with applications in robotics and mechanism theory

Müller, A. (2019) · Mechanism and Machine Theory · doi:10.1016/j.mechmachtheory.2019.103594 · Cited by 60

Reconfiguration Principles and Strategies for Reconfigurable Mechanisms

Kuo, C., Dai, J. S., & Yan, H. (2012) · Research Portal (King's College London) · Cited by 56

Reconfiguration Analysis of Multimode Single-Loop Spatial Mechanisms Using Dual Quaternions

Kong, X. (2017) · Journal of Mechanisms and Robotics · doi:10.1115/1.4037111 · Cited by 56

Analytic Geometry and Singularities of Mechanisms

Lerbet, J. (1998) · ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik · doi:10.1002/(sici)1521-4001(199810)78:10 · Cited by 50

Discontinuously Movable Seven-Link Mechanisms Via Group-Algebraic Approach

Lee, C.-C., & Hervé, J. M. (2005) · Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science · doi:10.1243/095440605x31436 · Cited by 48

Branching singularities in kinematotropic parallel mechanisms

Gogu, G. (2009) · Springer eBooks · doi:10.1007/978-3-642-01947-0_42 · Cited by 47

Geometry Constraint and Branch Motion Evolution of 3-PUP Parallel Mechanisms with Bifurcated Motion

Gan, D., & Dai, J. S. (2012) · Mechanism and Machine Theory · doi:10.1016/j.mechmachtheory.2012.09.011 · Cited by 42

Geometric constraints and motion branch variations for reconfiguration of single-loop linkages with mobility one

Zhang, K., & Dai, J. S. (2016) · Mechanism and Machine Theory · doi:10.1016/j.mechmachtheory.2016.08.006 · Cited by 37

Recursive higher-order constraints for linkages with lower kinematic pairs

Müller, A. (2016) · Mechanism and Machine Theory · doi:10.1016/j.mechmachtheory.2016.01.012 · Cited by 36

Verification of the higher order kinematic analyses equations

López-Custodio, P. C., Rico, J. M., Cervantes‐Sánchez, J. J., Perez-Soto, G. I., & Diez-Martínez, C. R. (2016) · European Journal of Mechanics - A/Solids · doi:10.1016/j.euromechsol.2016.09.010 · Cited by 35

First- and Second-Order Kinematics-Based Constraint System Analysis and Reconfiguration Identification for the Queer-Square Mechanism

Kang, X., Zhang, X. S., & Dai, J. S. (2018) · Journal of Mechanisms and Robotics · doi:10.1115/1.4041486 · Cited by 31

Reconfigurable Mechanisms From the Intersection of Surfaces

López-Custodio, P. C., Rico, J. M., Cervantes‐Sánchez, J. J., & Perez-Soto, G. I. (2015) · Journal of Mechanisms and Robotics · doi:10.1115/1.4032097 · Cited by 30

Branch Reconfiguration of Bricard Linkages Based on Toroids Intersections: Plane-Symmetric Case

López-Custodio, P. C., Dai, J. S., & Rico, J. M. (2018) · Journal of Mechanisms and Robotics · doi:10.1115/1.4039002 · Cited by 30

Singular Configurations of Mechanisms and Manipulators

Bohigas, O. (2019) · Courses and lectures · doi:10.1007/978-3-030-05219-5 · Cited by 28

Type Synthesis of Variable Degrees-of-Freedom Parallel Manipulators With Both Planar and 3T1R Operation Modes

Kong, X. (2012) · doi:10.1115/detc2012-70621 · Cited by 26

Branch Reconfiguration of Bricard Linkages Based on Toroids Intersections: Line-Symmetric Case

López-Custodio, P. C., Dai, J. S., & Rico, J. M. (2018) · Journal of Mechanisms and Robotics · doi:10.1115/1.4038981 · Cited by 26

A synthesis method for 1-DOF mechanisms with a cusp in the configuration space

López-Custodio, P. C., Müller, A., Rico, J. M., & Dai, J. S. (2019) · Mechanism and Machine Theory · doi:10.1016/j.mechmachtheory.2018.09.008 · Cited by 24

Kinematical analysis of Wunderlich mechanism

Arponen, T., Piipponen, S., & Tuomela, J. (2013) · Mechanism and Machine Theory · doi:10.1016/j.mechmachtheory.2013.06.011 · Cited by 21

Configuration analysis of the Schatz linkage

Lee, C. C., & Dai, J. S. (2003) · Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science · doi:10.1243/095440603767764426 · Cited by 21

Reconfigurable Chains of Bifurcating Type III Bricard Linkages

Lü, S., Zlatanov, D., Ding, X., Zoppi, M., & Guest, S. D. (2015) · Mechanisms and machine science · doi:10.1007/978-3-319-23327-7_1 · Cited by 18

Local Analysis of Helicoid–Helicoid Intersections in Reconfigurable Linkages

López-Custodio, P. C., Rico, J. M., & Cervantes‐Sánchez, J. J. (2017) · Journal of Mechanisms and Robotics · doi:10.1115/1.4035682 · Cited by 13

Local Investigation of Mobility and Singularities of Linkages

Müller, A. (2019) · Courses and lectures · doi:10.1007/978-3-030-05219-5_5 · Cited by 13

Local Analysis of Singular Configurations of Open and Closed Loop Manipulators

Müller, A. (2002) · Multibody System Dynamics · doi:10.1023/a:1020969529920 · Cited by 12

On Regular Kinematotropies

Müller, A., & Piipponen, S. (2015) · DMG-Lib Digital Mechanism and Gear Library · doi:10.6567/iftomm.14th.wc.os2.046 · Cited by 10

A Novel Method for Constructing Multi-Mode Deployable Polyhedron Mechanisms Using Symmetric Spatial RRR Compositional Units

Wang, J., & Kong, X. (2018) · doi:10.1115/detc2018-85100 · Cited by 10

Various types of RC// RC―― -like linkages and the discontinuously movable Koenigs joint

Lee, C.-C., & Hervé, J. M. (2015) · Mechanism and Machine Theory · doi:10.1016/j.mechmachtheory.2015.06.012 · Cited by 9

Design of a Variable-Mobility Linkage Using the Bohemian Dome

López-Custodio, P. C., & Dai, J. S. (2018) · doi:10.1115/detc2018-86004 · Cited by 7

The Metamorphic Bennett Linkages

Lee, C.-C., & Hervé, J. M. (2015) · DMG-Lib Digital Mechanism and Gear Library · Cited by 4

Analytical Kinematics of Overconstrained 20-Link 24R Mechanism: Branches with One, Two and Three Degrees of Freedom

Peisach, E. (1998) · Springer eBooks · doi:10.1007/978-94-015-9064-8_30 · Cited by 3

Higher-Order Local Analysis of Kinematic Singularities of Lower Pair Linkages

Müller, A. (2017) · doi:10.1115/detc2017-67039 · Cited by 2

Kinematic Analysis of Multi-4-Bar Mechanisms Using Algebraic Geometry

Piipponen, S., Hyry, E., & Arponen, T. (2017) · doi:10.1115/detc2017-67250 · Cited by 2

Motion singularity analysis of the thick-panel kirigami

Wang, C., Li, J., & Zhang, D. (2022) · Mechanism and Machine Theory · doi:10.1016/j.mechmachtheory.2022.105162 · Cited by 21

Synthesis of asymmetric parallel mechanism with multiple 3-DOF motion modes

Liu, W., & Liu, H. (2022) · Advances in Mechanical Engineering · doi:10.1177/16878140221075309 · Cited by 11

Mechanism singularities and shakiness from an algebraic viewpoint

Li, Z., & Müller, A. (2023) · Mechanism and Machine Theory · doi:10.1016/j.mechmachtheory.2023.105510 · Cited by 10

Deformable Morphing and Multivariable Stiffness in the Evolutionary Robotics

Feng, H., Xue, Y., Li, H., Tang, Z., Wang, W., Wei, Z., Zeng, G., Li, M., & Dai, J. S. (2023) · International Journal of Automotive Manufacturing and Materials · doi:10.53941/ijamm.2023.100013 · Cited by 7

Thermal Fluctuations of Singular Bar-Joint Mechanisms

Mannattil, M., Schwarz, J. M., & Santangelo, C. D. (2022) · Physical Review Letters · doi:10.1103/physrevlett.128.208005 · Cited by 7

Identification of Non-Transversal Motion Bifurcations of Linkages

Müller, A., López-Custodio, P. C., & Dai, J. S. (2021) · Journal of Mechanisms and Robotics · doi:10.1115/1.4049658 · Cited by 5

Identification of Non-Transversal Bifurcations of Linkages

Müller, A., López-Custodio, P. C., & Dai, J. S. (2020) · doi:10.1115/detc2020-22301 · Cited by 1

Branch Reconfiguration of Bricard Linkages Based on Toroids Intersections: Plane-Symmetric Case

López-Custodio, P. C., Dai, J. S., & Rico, J. M. (2018) · Journal of Mechanisms and Robotics · doi:10.1115/1.4039002 · Cited by 30

Kinematic Tangent Cone – A useful Concept for the local Mobility and Singularity Analysis

Müller, A. (2019) · Mechanisms and machine science · doi:10.1007/978-3-030-20131-9_34 · Cited by 3

Identification of Singularities and Real and Complex Solution Varieties of the Loop Constraints of Linkages Using the Kinematic Tangent Cone

Müller, A., & Li, Z. (2023) · doi:10.1115/detc2023-114638