Planar Linkage Synthesis for Mixed Motion, Path and Function Generation Using Poles and Rotation Angles

Four Bar Linkage ◽

Selection Of

The kinematic synthesis of planar linkage mechanisms has traditionally been broken into the categories of motion, path and function generation. Each of these categories of problems has been solved separately. Many problems in engineering practice require some combination of these problem types. For example, a problem requiring coupler points and/or poses in addition to specific input and/or output link angles that correspond to those positions. A limited amount of published work has addressed some specific underconstrained combinations of these problems. This paper presents a general graphical method for the synthesis of a four bar linkage to satisfy any combination of these exact synthesis problems that is not over constrained. The approach is to consider the constraints imposed by the target positions on the linkage through the poles and rotation angles. These pole and rotation angle constraints are necessary and sufficient conditions to meet the target positions. After the constraints are made, free choices which may remain can be explored by simply dragging a fixed pivot, a moving pivot or a pole in the plane. The designer can thus investigate the family of available solutions before making the selection of free choices to satisfy other criteria. The fully constrained combinations for a four bar linkage are given and sample problems are solved for several of them.

Planar Linkage Synthesis for Mixed Motion, Path, and Function Generation Using Poles and Rotation Angles1

Journal of Mechanisms and Robotics ◽

10.1115/1.4039064 ◽

2018 ◽

Vol 10 (2) ◽

Cited By ~ 1

Author(s):

Ronald A. Zimmerman

Keyword(s):

Sufficient Conditions ◽

Motion Path ◽

Engineering Practice ◽

Function Generation ◽

Problem Types ◽

The Family ◽

And Function ◽

Four Bar Linkage ◽

Selection Of

The kinematic synthesis of planar linkage mechanisms has traditionally been broken into the categories of motion, path, and function generation. Each of these categories of problems has been solved separately. Many problems in engineering practice require some combination of these problem types. For example, a problem requiring coupler points and/or poses in addition to specific input and/or output link angles that correspond to those positions. A limited amount of published work has addressed some specific underconstrained combinations of these problems. This paper presents a general graphical method for the synthesis of a four bar linkage to satisfy any combination of these exact synthesis problems that is not overconstrained. The approach is to consider the constraints imposed by the target positions on the linkage through the poles and rotation angles. These pole and rotation angle constraints (PRCs) are necessary and sufficient conditions to meet the target positions. After the constraints are made, free choices which may remain can be explored by simply dragging a fixed pivot, a moving pivot, or a pole in the plane. The designer can thus investigate the family of available solutions before making the selection of free choices to satisfy other criteria. The fully constrained combinations for a four bar linkage are given and sample problems are solved for several of them.

Using binary operations to construct a transitive set of block transformations

Discrete Mathematics and Applications ◽

10.1515/dma-2020-0035 ◽

2020 ◽

Vol 30 (6) ◽

pp. 375-389

Author(s):

Igor V. Cherednik

Keyword(s):

Binary Operation ◽

Sufficient Conditions ◽

Binary Operations ◽

The Family ◽

Transitive Set ◽

AbstractWe study the set of transformations {ΣF : F∈ 𝓑∗(Ω)} implemented by a network Σ with a single binary operation F, where 𝓑∗(Ω) is the set of all binary operations on Ω that are invertible as function of the second variable. We state a criterion of bijectivity of all transformations from the family {ΣF : F∈ 𝓑∗(Ω)} in terms of the structure of the network Σ, identify necessary and sufficient conditions of transitivity of the set of transformations {ΣF : F∈ 𝓑∗(Ω)}, and propose an efficient way of verifying these conditions. We also describe an algorithm for construction of networks Σ with transitive sets of transformations {ΣF : F∈ 𝓑∗(Ω)}.

A Direct Rotatability Criterion for Spherical Four-Bar Linkages

Journal of Mechanical Design ◽

10.1115/1.2826726 ◽

1995 ◽

Vol 117 (4) ◽

pp. 597-600 ◽

Cited By ~ 8

Author(s):

K. C. Gupta ◽

R. Ma

Keyword(s):

Sufficient Conditions ◽

Absolute Value ◽

The Difference ◽

Four Bar Linkage

The necessary and sufficient conditions for the full input rotatability in a spherical four-bar linkage are proved. The direct criterion is: for all twist angles α in the range [0, π], the excess (deficit) of the sum of the frame and input twist angles over (from) π should, in absolute value, be greater than that for the coupler and follower twist angles; the difference between the follower and input twist angles, in absolute value, should be greater than that for the coupler and follower twist angles. Application of the direct criterion to full rotatability of other links are discussed and some variations in the form of the criterion are developed.

A Direct Rotatability Criterion for Spherical Four-Bar Linkages

23rd Biennial Mechanisms Conference: Mechanism Synthesis and Analysis ◽

10.1115/detc1994-0206 ◽

1994 ◽

Author(s):

R. Ma ◽

K. C. Gupta

Keyword(s):

Sufficient Conditions ◽

Absolute Value ◽

The Difference ◽

Four Bar Linkage

Abstract The necessary and sufficient conditions for the full input rotatability in a spherical four bar linkage are proved. The direct criterion is: for all twist angles α in the range [0, π], the excess (deficit) of the sum of the frame and input twist angles over (from) π should, in absolute value, be greater than that for the coupler and follower twist angles; the difference between the follower and input twist angles, in absolute value, should be greater than that for the coupler and follower twist angles. Application of the direct criterion to full rotatability of other links are discussed and some variations in the form of the criterion are developed.

Gaps in Discrete Random Samples

Journal of Applied Probability ◽

10.1017/s0021900200006124 ◽

2009 ◽

Vol 46 (04) ◽

pp. 1038-1051 ◽

Cited By ~ 1

Author(s):

Rudolf Grübel ◽

Paweł Hitczenko

Keyword(s):

Analysis Of Algorithms ◽

Sufficient Conditions ◽

Borderline Case ◽

Convergence In Probability ◽

Enumerative Combinatorics ◽

Random Samples ◽

The Family ◽

Heavy Tailed ◽

Convergence Almost Surely ◽

Let (X i ) i∈ℕ be a sequence of independent and identically distributed random variables with values in the set ℕ0 of nonnegative integers. Motivated by applications in enumerative combinatorics and analysis of algorithms we investigate the number of gaps and the length of the longest gap in the set {X 1,…,X n } of the first n values. We obtain necessary and sufficient conditions in terms of the tail sequence (q k ) k∈ℕ0 , q k =P(X 1≥ k), for the gaps to vanish asymptotically as n→∞: these are ∑ k=0 ∞ q k+1/q k <∞ and limk→∞ q k+1/q k =0 for convergence almost surely and convergence in probability, respectively. We further show that the length of the longest gap tends to ∞ in probability if q k+1/q k → 1. For the family of geometric distributions, which can be regarded as the borderline case between the light-tailed and the heavy-tailed situations and which is also of particular interest in applications, we study the distribution of the length of the longest gap, using a construction based on the Sukhatme–Rényi representation of exponential order statistics to resolve the asymptotic distributional periodicities.

Fractal Behavior of a Ternary 4-Point Rational Interpolation Subdivision Scheme

Mathematical and Computational Applications ◽

10.3390/mca23040065 ◽

2018 ◽

Vol 23 (4) ◽

pp. 65 ◽

Cited By ~ 3

Author(s):

Kaijun Peng ◽

Jieqing Tan ◽

Zhiming Li ◽

Li Zhang

Keyword(s):

Singular Point ◽

Sufficient Conditions ◽

Rational Interpolation ◽

Subdivision Scheme ◽

Fractal Curve ◽

Rational Scheme ◽

Special Cases ◽

Parameter Values ◽

Selection Of

In this paper, a ternary 4-point rational interpolation subdivision scheme is presented, and the necessary and sufficient conditions of the continuity are analyzed. The generalization incorporates existing schemes as special cases: Hassan–Ivrissimtzis’s scheme, Siddiqi–Rehan’s scheme, and Siddiqi–Ahmad’s scheme. Furthermore, the fractal behavior of the scheme is investigated and analyzed, and the range of the parameter of the fractal curve is the neighborhood of the singular point of the rational scheme. When the fractal curve and surface are reconstructed, it is convenient for the selection of parameter values.

AUTOMORPHISMS OF THE UHF ALGEBRA THAT DO NOT EXTEND TO THE CUNTZ ALGEBRA

Journal of the Australian Mathematical Society ◽

10.1017/s1446788711001017 ◽

2010 ◽

Vol 89 (3) ◽

pp. 309-315 ◽

Cited By ~ 5

Author(s):

ROBERTO CONTI

Keyword(s):

Sufficient Conditions ◽

Extension Property ◽

Cuntz Algebra ◽

Maximal Abelian Subalgebra ◽

Abelian Subalgebra ◽

Matrix Algebras ◽

The Family ◽

The Matrix ◽

Inner Automorphisms ◽

AbstractThe automorphisms of the canonical core UHF subalgebra ℱn of the Cuntz algebra 𝒪n do not necessarily extend to automorphisms of 𝒪n. Simple examples are discussed within the family of infinite tensor products of (inner) automorphisms of the matrix algebras Mn. In that case, necessary and sufficient conditions for the extension property are presented. Also addressed is the problem of extending to 𝒪n the automorphisms of the diagonal 𝒟n, which is a regular maximal abelian subalgebra with Cantor spectrum. In particular, it is shown that there exist product-type automorphisms of 𝒟n that do not extend to (possibly proper) endomorphisms of 𝒪n.

The distribution of prime ideals of a Dedekind domain

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972700044063 ◽

1974 ◽

Vol 11 (3) ◽

pp. 429-441 ◽

Cited By ~ 20

Author(s):

Anne P. Grams

Keyword(s):

Class Group ◽

Sufficient Conditions ◽

Torsion Group ◽

Dedekind Domain ◽

Prime Ideals ◽

Class Groups ◽

Maximal Ideals ◽

The Family ◽

Let G be an abelian group, and let S be a subset of G. Necessary and sufficient conditions on G and S are given in order that there should exist a Dedekind domain D with class group G with the property that S is the set of classes that contain maximal ideals of D. If G is a torsion group, then S is the set of classes containing the maximal ideals of D if and only if S generates G. These results are used to determine necessary and sufficient conditions on a family {Hλ} of subgroups of G in order that there should exist a Dedekind domain D with class group G such that {G/Hλ} is the family of class groups of the set of overrings of D. Several applications are given.

Defect Effect of Bi-infinite Words in the Two-element Case

Discrete Mathematics & Theoretical Computer Science ◽

10.46298/dmtcs.279 ◽

2001 ◽

Vol Vol. 4 no. 2 ◽

Author(s):

Ján Maňuch

Keyword(s):

Sufficient Conditions ◽

Finite Alphabet ◽

Infinite Words ◽

Infinite Word ◽

The Family ◽

International Audience ◽

Primitive Roots ◽

Element Set

International audience Let X be a two-element set of words over a finite alphabet. If a bi-infinite word possesses two X-factorizations which are not shiftequivalent, then the primitive roots of the words in X are conjugates. Note, that this is a strict sharpening of a defect theorem for bi-infinite words stated in \emphKMP. Moreover, we prove that there is at most one bi-infinite word possessing two different X-factorizations and give a necessary and sufficient conditions on X for the existence of such a word. Finally, we prove that the family of sets X for which such a word exists is parameterizable.

Greedoids on vertex sets of B-joins of graphs

Carpathian Journal of Mathematics ◽

10.37193/cjm.2014.03.10 ◽

2014 ◽

Vol 30 (3) ◽

pp. 335-344

Author(s):

VADIM E. LEVIT ◽

◽

EUGEN MANDRESCU ◽

Keyword(s):

Bipartite Graph ◽

Sufficient Conditions ◽

Local Maximum ◽

Stable Set ◽

Stable Sets ◽

The Family ◽

Maximum Stable Set ◽

Vertex Set ◽

Vertex Sets

Let Ψ(G) be the family of all local maximum stable sets of graph G, i.e., S ∈ Ψ(G) if S is a maximum stable set of the subgraph induced by S ∪ N(S), where N(S) is the neighborhood of S. It was shown that Ψ(G) is a greedoid for every forest G [15]. The cases of bipartite graphs, triangle-free graphs, and well-covered graphs, were analyzed in [16, 17, 18, 19, 20, 24]. If G1, G2 are two disjoint graphs, and B is a bipartite graph having E(B) as an edge set and bipartition {V (G1), V (G2)}, then by B-join of G1, G2 we mean the graph B (G1, G2) whose vertex set is V (G1) ∪ V (G2) and edge set is E(G1) ∪ E(G2) ∪ E (B). In this paper we present several necessary and sufficient conditions for Ψ(B (G1, G2)) to form a greedoid, an antimatroid, and a matroid, in terms of Ψ(G1), Ψ(G2) and E (B).