A New Approach for Locating the Instantaneous Centers of Zero Velocity for 1-DOF Planar Linkages

2018 ◽  
Author(s):  
Nadim Diab
Keyword(s):  
Degree Of Freedom ◽  
Planar Mechanisms ◽  
New Approach ◽  
Zero Velocity ◽  
Graphical Technique ◽  
Instantaneous Center ◽  
Planar Linkages ◽  
Consistent Approach

This paper presents a new graphical technique to locate the secondary instantaneous centers of zero velocity (ICs) for one-degree-of-freedom (1-DOF) kinematically indeterminate planar mechanisms. The proposed approach is based on transforming the 1-DOF mechanism into a 2-DOF counterpart by converting any ground-pivoted ternary link into two ground-pivoted binary links. Fixing each of these two new binary links, one at a time, results in two different 1-DOF mechanisms where the intersection of the loci of their instantaneous centers will determine the location of the desired instantaneous center for the original 1-DOF mechanism. This single and consistent approach proved to be successful in locating the ICs of various mechanisms reported in the literature that required different techniques to reach the same results obtained herein.

New Synthesis Approach for Expandable Polyhedral Linkages

2014 ◽  
Author(s):  
Ying Zhang ◽  
Hai-Jun Su ◽  
Qizheng Liao ◽  
Shimin Wei ◽  
Weiqing Li
Keyword(s):  
Screw Theory ◽  
Degree Of Freedom ◽  
New Approach ◽  
And Topology ◽  
New Synthesis ◽  
The One ◽  
Planar Linkages ◽  
Synthesis Approach ◽  
Topology Graph

This paper presents a new synthesis approach for expandable polyhedral linkages, which are synthesized by inserting appropriate link groups into the faces of polyhedron and interconnecting them by a special composite hinges (called gusset by K. Wohlhart). The overconstrained expandable polyhedral linkages are movable with one degree of freedom (DOF).The link groups are single DOF scaling planar linkages. The gussets are multiple rotary joints whose axes converge at the corresponding vertices of the polyhedron and the number of the rotary joints equals the one of the faces which meet at the vertices. This new approach is suitable for any polyhedron whatever is regular or irregular polyhedron. To verify this new approach, the expandable regular hexahedral linkage is modeled in the SolidWorks and its mobility are studied based on screw theory and topology graph.

Expandable Polyhedral Mechanisms Based on Polygonal One-Degree-of-Freedom Faces

2006 ◽  
Vol 220 (7) ◽  
pp. 1011-1018 ◽  
Author(s):  
C M Gosselin ◽  
D Gagnon-Lachance
Keyword(s):  
Degree Of Freedom ◽  
Platonic Solids ◽  
Planar Mechanisms ◽  
Maximum Expansion ◽  
Theoretical Maximum ◽  
New Family ◽  
Regular Polyhedra ◽  
Simulation Results ◽  
Planar Linkages

In this article, a new family of expandable mechanisms is presented. The proposed mechanisms are expandable polyhedra built using one-degree-of-freedom (one-DOF) planar linkages. The latter planar linkages have the shape of polygons and can be expanded while preserving their shape in any of their configurations. The planar mechanisms are used to form the faces of a polyhedron. They are assembled using spherical joints at the vertices of the polyhedron. The result is a one-DOF movable polyhedron which can be expanded while preserving its shape. The application of the principle on regular polyhedra is first presented. For the five Platonic solids, theoretical maximum expansion ratios are computed, simulation results are given, and two prototypes are shown. Then, two additional examples are provided to illustrate the application of the principle to irregular polyhedra.

scholarly journals A Screw Theory Approach to Computing the Instantaneous Rotation Centers of Indeterminate Planar Linkages

Robotics ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 6
Author(s):  
Juan Ignacio Valderrama-Rodríguez ◽  
José M. Rico ◽  
J. Jesús Cervantes-Sánchez ◽  
Ricardo García-García
Keyword(s):  
Screw Theory ◽  
Bilinear Forms ◽  
Theory Approach ◽  
Algebraic Equations ◽  
Euclidean Group ◽  
Planar Mechanisms ◽  
New Approach ◽  
Planar Linkages ◽  
The 19Th Century

This paper presents a screw theory approach for the computation of the instantaneous rotation centers of indeterminate planar linkages. Since the end of the 19th century, the determination of the instantaneous rotation, or velocity centers of planar mechanisms has been an important topic in kinematics that has led to the well-known Aronhold–Kennedy theorem. At the beginning of the 20th century, it was found that there were planar mechanisms for which the application of the Aronhold–Kennedy theorem was unable to find all the instantaneous rotation centers (IRCs). These mechanisms were denominated complex or indeterminate. The beginning of this century saw a renewed interest in complex or indeterminate planar mechanisms. In this contribution, a new and simpler screw theory approach for the determination of indeterminate rotation centers of planar linkages is presented. The new approach provides a simpler method for setting up the equations. Furthermore, the algebraic equations to be solved are simpler than the ones published to date. The method is based on the systematic application of screw theory, isomorphic to the Lie algebra, se(3), of the Euclidean group, SE(3), and the invariant symmetric bilinear forms defined on se(3).

The Radius of Curvature of a Coupler Curve of the Single Flier Eight-Bar Linkage

2003 ◽  
Author(s):  
Gordon R. Pennock ◽  
Edward C. Kinzel
Keyword(s):  
Radius Of Curvature ◽  
Operating Speed ◽  
Velocity Analysis ◽  
Zero Velocity ◽  
Original Contribution ◽  
Graphical Technique ◽  
Curvature Theory ◽  
Instantaneous Center ◽  
Insight Into ◽  
Geometric Effects

The paper begins with a graphical technique to locate the pole; i.e., the point in the plane of motion which is coincident with the instantaneous center of zero velocity of the coupler link. Since the single flier linkage is indeterminate, the Aronhold-Kennedy theorem cannot locate this instantaneous center of zero velocity. The technique that is presented here is believed to be an original contribution to the kinematics literature and will provide geometric insight into the velocity analysis of an indeterminate linkage. The paper then presents an analytical method, referred to as the method of kinematic coefficients, to determine the radius of curvature and the center of curvature of the path traced by an arbitrary coupler point of the single flier eight-bar linkage. This method has proved useful in curvature theory since it separates the geometric effects of the linkage from the operating speed of the linkage.

Singularity Analysis of Multi-DOF Planar Mechanisms

2007 ◽  
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
Motion Control ◽  
Singularity Analysis ◽  
Degree Of Freedom ◽  
Static Behavior ◽  
Planar Mechanisms ◽  
New Approach ◽  
Singular Configurations

Singular configurations (singularities) are mechanism configurations where the instantaneous kinematics is locally undetermined. Since the indetermination of the instantaneous kinematics causes serious problems both to the static behavior and to the motion control of the mechanism, the research of all the singularities (singularity analysis) is a mandatory step during the design of mechanisms. This paper presents a new approach to implement the singularity analysis of planar mechanisms. The proposed technique extends the use of the instant center properties to the singularity analysis of planar mechanisms with more than one degree of freedom (dof). It exploits the results of previous works by the author in which a geometric and analytic technique has been presented to address the singularity analysis of single-dof planar mechanisms.

A Graphical Method to Find the Secondary Instantaneous Centers of Zero Velocity for the Double Butterfly Linkage

2003 ◽  
Vol 125 (2) ◽  
pp. 268-274 ◽  
Author(s):  
David E. Foster ◽  
Gordon R. Pennock
Keyword(s):  
Graphical Method ◽  
Degree Of Freedom ◽  
Second Step ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Zero Velocity ◽  
Graphical Technique ◽  
The Absolute

The Aronhold-Kennedy theorem cannot locate all of the instantaneous centers of zero velocity for a planar, single-degree-of-freedom, indeterminate linkage. This paper presents a graphical technique that will locate the secondary instantaneous centers of zero velocity for a well-known indeterminate linkage; namely, the double butterfly linkage. Only one of the secondary instant centers of this eight-bar linkage needs to be located with the proposed technique; the remaining instant centers can then be located using the Aronhold-Kennedy theorem. The first step in the graphical method is to regard the double butterfly linkage as two six-bar linkages. This is accomplished by replacing the ternary link pinned to the ground by two binary links, removing the pin which connects the two coupler links, and attaching a slider to each coupler link at the coupler pin. The second step is to reduce two of the five-bar loops of the double butterfly linkage to four-bar loops by instantaneously freezing the aforementioned binary links. The paper shows how these two important steps are used to locate the absolute instant centers for the two coupler links of this indeterminate eight-bar linkage.

VariableZ0antenna technology: a new approach for IoT wireless

2014 ◽  
Vol 7 (2) ◽  
pp. 195-203 ◽  
Author(s):  
Richard A. Formato
Keyword(s):  
Internet Of Things ◽  
Degree Of Freedom ◽  
The Internet ◽  
Simple Design ◽  
Wireless Devices ◽  
Decision Space ◽  
New Approach ◽  
Optimization Methodology ◽  
The Internet Of Things

Variable Z0(VZ0) antenna technology is a new design or optimization methodology applicable to any antenna on any platform designed or optimized with any procedure. It should be particularly useful for wireless devices populating the Internet of Things. VZ0expands the design or decision space by adding another degree of freedom invariably leading to better antennas. A simple design example illustrates its effectiveness.

PREDICTION OF MUSCLE FORCES USING STATIC OPTIMIZATION FOR DIFFERENT CONTRACTILE CONDITIONS

2013 ◽  
Vol 13 (03) ◽  
pp. 1350022 ◽  
Author(s):  
YUNUS ZIYA ARSLAN ◽  
AZIM JINHA ◽  
MOTOSHI KAYA ◽  
WALTER HERZOG
Keyword(s):  
Cost Function ◽  
Fiber Type ◽  
Degree Of Freedom ◽  
Muscle Forces ◽  
Cross Sectional ◽  
Satisfactory Description ◽  
New Approach ◽  
Force Sharing ◽  
Synergistic Muscles ◽  
The Cost

In this study, we introduced a novel cost function for the prediction of individual muscle forces for a one degree-of-freedom musculoskeletal system. Unlike previous models, the new approach incorporates the instantaneous contractile conditions represented by the force-length and force-velocity relationships and accounts for physiological properties such as fiber type distribution and physiological cross-sectional area (PCSA) in the cost function. Using this cost function, it is possible to predict experimentally observed features of force-sharing among synergistic muscles that cannot be predicted using the classical approaches. Specifically, the new approach allows for predictions of force-sharing loops of agonistic muscles in one degree-of-freedom systems and for simultaneous increases in force in one muscle and decreases in a corresponding agonist. We concluded that the incorporation of the contractile conditions in the weighting of cost functions provides a natural way to incorporate observed force-sharing features in synergistic muscles that have eluded satisfactory description.

A Generalized Approach for the Kinematic Analysis of Planar Mechanisms

1995 ◽  
Vol 209 (4) ◽  
pp. 237-244
Author(s):  
D J A Simpson ◽  
J E L Simmons ◽  
G Moldovean
Keyword(s):  
Computer Program ◽  
Analytical Method ◽  
Building Block ◽  
Kinematic Analysis ◽  
Displacement Velocity ◽  
Planar Mechanisms ◽  
New Approach ◽  
Wide Range ◽  
Complex Mechanisms

This paper describes a new approach to the kinematic analysis of planar mechanisms. The basis of the analytical method is a generic four-bar sub-mechanism which is used as the single building block from which other composite mechanisms may be created. A computer program has been written embodying this method and has been demonstrated to operate successfully providing animated displays of displacement, velocity and acceleration diagrams for a wide range of complex mechanisms.

A New Approach for Exact/Approximate Point Synthesis of Planar Mechanisms

2005 ◽  
Author(s):  
Ahmad Smaili ◽  
Nadim Diab
Keyword(s):  
Synthesis Method ◽  
Dimensional Synthesis ◽  
Gradient Search ◽  
Planar Mechanisms ◽  
Simple Method ◽  
New Approach ◽  
Optimum Synthesis ◽  
Approximate Synthesis ◽  
Optimum Solution ◽  
Synthesis Approach

The aim of this article is to provide a simple method to solve the mixed exact-approximate dimensional synthesis problem of planar mechanism. The method results in a mechanism that can traverse a closed path with the choice of any number of exact points while the rest are approximate points. The algorithm is based on optimum synthesis rather than on precision position methods. Ant-gradient search is applied on an objective function based on log10 of the error between the desired positions and those generated by the optimum solution. The log10 function discriminates on the side of generating miniscule errors (on the order of 10−14) at the exact points while allowing for higher errors at the approximate positions. The algorithm is tested by way of five examples. One of these examples was used to test exact/approximate synthesis method based on precision point synthesis approach.

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