It is proved that the new formula is correct, general, simple and effective through the mobility analysis of several different kinds of planar mechanisms.
Huang Zhen, Liu Jingfang, Zeng Daxing. Symposia Proceedings (Cat. This paper describes techniques, based on polynomial continuation, for numerically solving systems having higher-dimensional solution sets, and focuses on cases of exceptional mechanisms, which have a higher degree of freedom of motion than predicted by their mobility. Computational Algorithm for Determining the Generic Mobility of Floating Planar and Spherical Linkages, A Novel Combinatorial Algorithm for Determining the Generic/Topological Mobility of Planar and Spherical Mechanisms, Mechanism mobility and a local dimension test, Combinatorial Algorithm for Determination of Topological Mobility of Floating Planar and Spherical Linkages, Mobility Determination Of Mechanisms Based On Rigidity Theory, Degrees of Freedom Analysis of Mechanisms using the New Zebra Crossing Method, A Unified Concept for the Graph Representation of Constraints in Mechanisms, Generic mobility of rigid body mechanisms, Degree of freedom analysis of hexapod wall-climbing robot, On Calculating the Degrees of Freedom or Mobility of Overconstrained Linkages: Single-Loop Exceptional Linkages, Mobility of mechanisms: a critical review, A Kinematic Theory for Planar Hoberman and Other Novel Foldable Mechanisms, Lie Algebra and the Mobility of Kinematic Chains, Computation of the configuration degree of freedom of a spatial parallel mechanism by using reciprocal screw theory, Advances in Polynomial Continuation for Solving Problems in Kinematics, Self-motions of Griffis-Duffy type parallel manipulators, Evaluation of a Cartesian Parallel Manipulator, The numerical solution of systems of polynomials - arising in engineering and science, A new formula for predicting the mobility of spatial mechanisms is introduced. Advanced Spatial Mechanism [M]. Chebychev, Thorie des mecanismes connus sous le nom de paralllogrammes, 2ere partie[C], Mmoires prsents l Acadmie impriale des sciences de Saint-Ptersbourg par divers savants, 1869. IEEE International Conference on Robotics and Automation. In, In this paper, we present a kinematic theory for Hoberman and other similar foldable linkages. % A quick method for calculation of degrees of freedom in a mechanism is proposed and an algorithm is proposed which is used to determine the mobility from the zebra crossing diagram. No.00CH37065). 562-564. J, Freedom in machinery[M]. P.A. :V;m1ZLTNh =^DB)Gz4MBkd>Ch7ME=h/zMC?MG?V4@4]+<4GUh!]k:tZIf`X@y ~?AX2Gcq^ The knowledge of degree of freedom (referred as DOF) is indispensable before a parallel mechanism is designed, but the traditional Grubler-Kutzbach formula (referred as G-K formula) which is widely, This paper reformulates and extends the new, group theoretic, mobility criterion recently developed by the authors, (Rico, J. M., and Ravani, B., 2003, ASME J. Mech. International Conference on Mechanical Transmissions, Chongqing, China, Sept. 26-30, 2006: 799802. Structural mobility criteria, such as the well-known Chebychev-Kutzbach-Grbler (CKG) formula, give the correct topological mobility of a linkage (possibly of a certain class, e.g. Scientific.Net is a registered brand of Trans Tech Publications Ltd 2022 by Trans Tech Publications Ltd. All Rights Reserved, Leakage Analysis of a Synchronal Rotary Multiphase Pump, Study on Process Planning of Auto Body Welding Line Based on Digital Factory, A Method for Solving Stiffness of Finite Length Self-Acting Gas-Lubricated Journal Bearing, The Assessment of Cylinder Liner by HAZOP Analysis and Fuzzy Comprehensive Evaluation, General Formula of Mobility Calculation for Planar Mechanism, Orthogonal Experiment Design and Analysis on ABS Power in SLS, Analysis and Calculation of 3MW Wind-Turbine Main Shaft, Intervallic Coiflets for Numerical Calculation of Dynamic Stress Intensity Factor, GA-Based Optimal Design of Derricking Balance Mechanism of Bucket Wheel Stacker Reclaimer. planar, spherical, View 3 excerpts, cites methods and background.
They are not suitable for planar mechanism with virtual constraints and the number of general constraints equal to 4. General Formula of Mobility Calculation for Planar Advanced Materials Research Vols. A special type of parallel platform manipulator is investigated and it is shown that a large class among the proposed platform types is architecture singular and admits self motions from every point of its workspace. 
Instead of counting rigid links and the constraints between them, as is done in the usual Grubler-Kutzbach formulae, we count vertices and edges in a polyhedral model of the mechanism. z2rhch{=/C*"y=&Mwev[/|N;ZK&c+\.7xw4B0AU]K+%
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o{xk+\si2uE:lKen-K)b"O.A2ysK!g>cuB ~//C:c tBG:Orv>4[*G#G#txl?#wx?tgiC"J{;,=`98pwwuo Sci China Tech Sci, 2010, 53(6): 1598-1604. !K1qq#8*m]DB]8F0n Wpgx&UxaP/)MQ8-D(2gf|'X'Og//;O[F 'h(t
t\.$pol!;-. it aims at making generic statements. {ho/#9NpN 9S$hC(DBr!_(7T*Ufn The theory presented provides for a computational approach that would allow efficient automation of the new group-theoretic mobility criterion developed recently by two of the authors of this publication. Beijing: Higher Education Press, 2006. (in Chinese). 
{r/G+@y. A general methodology for mobility analysis of mechanisms based on constraint screw theory[J]. Zhang Yitong, Mu Dejun. 9@=8{ @A{zJP97#y7J0
NMS 3dUAe-#BKQ{]p;+)a1gG;8;j:6-H/YnWg6qCO[rrt? An extension of Laman's theorem is introduced that enables application of the algorithm to any planar or spherical mechanism with higher and lower holonomic kinematic pairs and multiple joints, and yields the redundantly constrained sub-linkages of a mechanism. Sci China Tech Sci, 2009, 52(5): 13371347. 2 0 obj By recognizing that the building blocks of such linkages can be modeled as planar linkages, different. planar, spherical. Phillips. Millennium Conference. https://doi.org/10.4028/www.scientific.net/AMR.562-564.654. [2] Des., 125, pp. To solve the problem, the new concepts of virtual loop, virtual-loop constraint and virtual pair are defined to establish a general f ormula for DOF of planar mechanism; the calculation method for virtual-loop constraint and the mobility of link-group are also given. Background: Polynomial Systems Homotopy Continuation Projective Spaces Probability One Polynomials of One Variable Other Methods Isolated Solutions: Coefficient-Parameter Homotopy Polynomial, By clicking accept or continuing to use the site, you agree to the terms outlined in our. A new 3-DOF translational parallel manipulator named a Cartesian Parallel Manipulator (CPM) that behaves like a conventional X-Y-Z Cartesian machine due to the orthogonal arrangement of the three supporting limbs is described. %PDF-1.6 New concept and new theory of mobility calculation for multi-loop mechanisms[J].
Zhang Y T, Lu L, Li Y W. Different expressions for the degrees of freedom of spatial mechanisms[C]/. [5] Sydney: Cambridge University Press, (1984).
The components of mechanism freedom and structure in mechanism elementary planar and spatial displacements planar algebraic curves infinitesimal planar kinematics planar displacements through three, Proceedings 2000 ICRA. o3\ox3&c+ca~7x~]6(3q~B- 9o=> wp{^186Ez6qxxxFK[GWO_|@|PFOk'u3sL~^|E FqIlgsq$noo;w.oGq/o[,xADAdATA? Mechanism theory is mainly concerned with the geometrical analysis but. Huang Zhen, Zhao Yongsheng, Zhao Tieshi. !2&fiBZ)n.n^>9:,Mh'S:%C+Y9yE%eiAJ Fi(mGO4-j!-O It is well known that the conventional formula underpredicts the mobility of certain exceptional classes of mechanisms, and in particular, does not easily accommodate compound spatial mechanisms that contain planar or spherical sub. [4] [1] Structural mobility criteria, such as the well-known Chebychev-Kutzbach-Grubler (CKG) formula, give the correct generic mobility of a linkage (possibly of a certain class, e.g. Rigidity theory deals mostly with the topological computation in mechanical systems, i.e. In the current and subsequent Chapters, a mobility principle based on the screw theory and modified G-K formulas is introduced, indicating that the mobility principle is really unified. J}P[R[A@}+*")(x"*"(mL4~=gRB*Z84g1%/#7sBn+63NvBZtZz| .h MM2i:K=Ups^?m,} S#A82gs7+BS>p~ 70-80). xy`E<3{f4M4mi [6]
A generalized and unified concept for the representation of constraints in mechanisms is introduced and this novel mixed constraint graph allows for computation of the correct generic (topological) mobility, and thus overcomes the problems of BB and BJ representations. Semantic Scholar is a free, AI-powered research tool for scientific literature, based at the Allen Institute for AI. [3] ?W!xDZFV??'s4dJ6.I)]rJ.-y$2,/l)GKZfh#7Q;vw?-g-,-KLG:r'KRP V-)4:~3Y~_/z