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A Linear Relaxation Technique for the Position Analysis of Multiloop Linkages
 IEEE TRANSACTIONS ON ROBOTICS
"... This paper presents a new method to isolate all configurations that a multiloop linkage can adopt. The problem is tackled by means of formulation and resolution techniques that fit particularly well together. The adopted formulation yields a system of simple equations (only containing linear, biline ..."
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Cited by 23 (15 self)
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This paper presents a new method to isolate all configurations that a multiloop linkage can adopt. The problem is tackled by means of formulation and resolution techniques that fit particularly well together. The adopted formulation yields a system of simple equations (only containing linear, bilinear, and quadratic monomials, and trivial trigonometric terms for the helical pair only) whose structure is later exploited by a branchandprune method based on linear relaxations. The method is general, as it can be applied to linkages with single or multiple loops with arbitrary topology, involving lower pairs of any kind, and complete, as all possible solutions get accurately bounded, irrespectively of whether the linkage is rigid or mobile.
Finding all real points of a complex curve
, 2006
"... An algorithm is given to compute the real points of the irreducible onedimensional complex components of the solution sets of systems of polynomials with real coefficients. The algorithm is based on homotopy continuation and the numerical irreducible decomposition. An extended application is made ..."
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Cited by 19 (10 self)
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An algorithm is given to compute the real points of the irreducible onedimensional complex components of the solution sets of systems of polynomials with real coefficients. The algorithm is based on homotopy continuation and the numerical irreducible decomposition. An extended application is made to GriffisDuffy platforms, a class of StewartGough platform robots. 2000 Mathematics Subject Classification. Primary 65H10; Secondary 65H20, 14Q99. Key words and phrases. Homotopy continuation, numerical algebraic geometry, real polynomial systems. In this article we give a numerical algorithm to find the real zero and
Box approximations of planar linkage configuration spaces
 ASME Journal of Mechanical Design
, 2007
"... This paper presents a numerical method able to compute all possible configurations of planar linkages. The procedure is applicable to rigid linkages (i.e., those that can only adopt a finite number of configurations) and to mobile ones (i.e., those that exhibit a continuum of possible configurations ..."
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Cited by 13 (11 self)
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This paper presents a numerical method able to compute all possible configurations of planar linkages. The procedure is applicable to rigid linkages (i.e., those that can only adopt a finite number of configurations) and to mobile ones (i.e., those that exhibit a continuum of possible configurations). The method is based on the fact that this problem can be reduced to finding the roots of a polynomial system of linear, quadratic, and hyperbolic equations, which is here tackled with a new strategy exploiting its structure. The method is conceptually simple and easy to implement, yet it provides solutions of the desired accuracy in short computation times. Experiments are included which show its performance on the double butterfly linkage and on larger linkages formed by the concatenation of basic patterns. 1
A Complete Method for Workspace Boundary Determination on General Structure Manipulators
"... Abstract—This paper introduces a new method for workspace boundary determination on general structure manipulators. The method uses a branchandprune technique to isolate a set of output singularities and then classifies the points on such a set according to whether they correspond to motion impedi ..."
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Abstract—This paper introduces a new method for workspace boundary determination on general structure manipulators. The method uses a branchandprune technique to isolate a set of output singularities and then classifies the points on such a set according to whether they correspond to motion impediments in the workspace. A detailed map of the workspace is obtained as a result, where all interior and exterior regions, together with the singularity and barrier sets that separate them, get clearly identified. The method can deal with open or closedchain manipulators, whether planar or spatial, and is able to take joint limits into account. Advantages over previous general methods based on continuation include the ability to converge to all boundary points, even in higher dimensional cases, and the fact that manual guidance with aprioriknowledge of the workspace is not required. Examples are included that show the performance of the method on benchmark problems documented in the literature, as well as on new ones unsolved so far. Index Terms—Branchandprune method, closedchain, kinematics, linear relaxation, mechanism design, multibody system, parallel robot, workspace determination. I.
On closedform solutions to the position analysis of Baranov trusses
 Mechanism and Machine Theory 50 (2012) 179
"... The exact position analysis of a planar mechanism reduces to compute the roots of its characteristic polynomial. Obtaining this polynomial usually involves, as a first step, obtaining a system of equations derived from the independent kinematic loops of the mechanism. Although conceptually simple, t ..."
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Cited by 2 (1 self)
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The exact position analysis of a planar mechanism reduces to compute the roots of its characteristic polynomial. Obtaining this polynomial usually involves, as a first step, obtaining a system of equations derived from the independent kinematic loops of the mechanism. Although conceptually simple, the use of kinematic loops for deriving characteristic polynomials leads to complex variable eliminations and, in most cases, trigonometric substitutions. As an alternative, a method based on bilateration has recently been shown to permit obtaining the characteristic polynomials of the threeloop Baranov trusses without relying on variable eliminations or trigonometric substitutions. This paper shows how this technique can be applied to solve the position analysis of all catalogued Baranov trusses. The characteristic polynomials of them all have been derived and, as a result, the maximum number of their assembly modes has been obtained. A comprehensive literature survey is also included.
DIMENSIONAL SYNTHESIS OF PLANAR SIXBAR LINKAGES BY MECHANICALLY CONSTRAIN A PRR SERIAL CHAIN
"... ABSTRACT In this paper, we consider the problem of designing planar sixbar linkages which can be driven by prismatic joints at its base. We explore various ways on how two RR chains can be used to constraint a PRR planar serial chain such that the system yields onedegree of freedom yet passes thr ..."
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ABSTRACT In this paper, we consider the problem of designing planar sixbar linkages which can be driven by prismatic joints at its base. We explore various ways on how two RR chains can be used to constraint a PRR planar serial chain such that the system yields onedegree of freedom yet passes through a set of five specified task positions. We formulate and solve the design equations as well as analyze the resulting planar sixbar linkage. We demonstrate the synthesis process with the design of the seat of a wheelchair such that it is able to transform itself to be used as a rehabilitation guide during rehabilitation.
Exact interval propagation for the efficient solution of planar linkages
"... Abstract — This paper presents an interval propagation algorithm for variables in singleloop linkages. Given allowed intervals of values for all variables, the algorithm provides, for every variable, the exact interval of values for which the linkage can actually be assembled. We show further how t ..."
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Abstract — This paper presents an interval propagation algorithm for variables in singleloop linkages. Given allowed intervals of values for all variables, the algorithm provides, for every variable, the exact interval of values for which the linkage can actually be assembled. We show further how this algorithm can be integrated in a branchandbound search scheme, in order to solve the position analysis of general multiloop linkages. Experimental results are included, comparing the method’s performance with that of previous techniques given for the same task.
Mechanism branches, turning curves, and critical points
"... This paper considers singledegreeoffreedom, closedloop linkages with a designated input angle and one design parameter. For a fixed value of the design parameter, a linkage has turning points (deadinput singularities), which break the motion curve into branches such that the motion along each ..."
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This paper considers singledegreeoffreedom, closedloop linkages with a designated input angle and one design parameter. For a fixed value of the design parameter, a linkage has turning points (deadinput singularities), which break the motion curve into branches such that the motion along each branch can be driven monotonically from the input. As the design parameter changes, the number of branches and their connections, in short the topology of the motion curve, may change at certain critical points. As the design parameter changes, the turning points sweep out a curve we call the “turning curve, ” and the critical points are the singularities in this curve with respect to the design parameter. The critical points have succinct geometric interpretations as transition linkages. We present a general method to compute the turning curve and its critical points. As an example, the method is used on a Stephenson II linkage. Additionally, the Stephenson III linkage is revisited where the input angle is able to rotate more than one revolution between singularities. This characteristic is associated with cusps on the turning point curve. 1
Pin Wang Research on Position Analysis of a Kind of NineLink Barranov Truss
"... The position analysis of a ninelink Barranov truss is finished by using ..."
Automated Generation of Linkage Loop Equations for Planar One DegreeofFreedom Linkages, Demonstrated up to 8Bar
"... In this paper, we present an algorithm that automatically creates the linkage loop equations for planar one degree of freedom, 1DOF, linkages of any topology with revolute joints, demonstrated up to 8 bar. The algorithm derives the linkage loop equations from the linkage adjacency graph by establis ..."
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In this paper, we present an algorithm that automatically creates the linkage loop equations for planar one degree of freedom, 1DOF, linkages of any topology with revolute joints, demonstrated up to 8 bar. The algorithm derives the linkage loop equations from the linkage adjacency graph by establishing a rooted cycle basis through a single common edge. Divergent and convergent loops are identified and used to establish the fixed angles of the ternary and higher links. Results demonstrate the automated generation of the linkage loop equations for the nine unique 6bar linkages with groundconnected inputs that can be constructed from the five distinct 6bar mechanisms, Watt III and Stephenson IIII. Results also automatically produced the loop equations for all 153 unique linkages with a groundconnected input that can be constructed from the 71 distinct 8bar mechanisms. The resulting loop equations enable the automatic derivation of the Dixon determinant for linkage kinematic analysis of the position of every possible assembly configuration. The loop equations also enable the automatic derivation of the Jacobian for singularity evaluation and tracking of a particular assembly configuration over the desired range of input angles. The methodology provides the foundation for the automated configuration analysis of every topology and every assembly configuration of 1DOF linkages with revolute joints up to 8 bar. The methodology also provides a foundation for automated configuration analysis of 10bar and higher linkages.