scholarly journals Closure to “Discussions of ‘A Kinematic Notation for Lower-Pair Mechanisms Based on Matrices’” (1956, ASME J. Appl. Mech., 23, pp. 151–153)

1956 ◽  
Vol 23 (1) ◽  
pp. 153
Author(s):  
J. Denavit ◽  
R. S. Hartenberg
Keyword(s):  
Lower Pair

A Kinematic Notation for Lower-Pair Mechanisms Based on Matrices

1955 ◽  
Vol 22 (2) ◽  
pp. 215-221
Author(s):  
J. Denavit ◽  
R. S. Hartenberg
Keyword(s):  
Matrix Algebra ◽  
Symbolic Notation ◽  
Lower Pair ◽  
Space Mechanisms ◽  
Kinematic Properties

Abstract A symbolic notation devised by Reuleaux to describe mechanisms did not recognize the necessary number of variables needed for complete description. A reconsideration of the problem leads to a symbolic notation which permits the complete description of the kinematic properties of all lower-pair mechanisms by means of equations. The symbolic notation also yields a method for studying lower-pair mechanisms by means of matrix algebra; two examples of application to space mechanisms are given.

A Dyad Search Algorithm for Solving Planar Linkages Using the Dyad Method

1992 ◽  
Author(s):  
Lofti Romdhane
Keyword(s):  
Search Algorithm ◽  
Class Ii ◽  
Graph Representation ◽  
Step Size ◽  
Lower Pair ◽  
Fast Solution ◽  
Complete Automation ◽  
Newton Raphson ◽  
Dyad Analysis ◽  
Planar Linkages

Abstract Based on graph representation of planar linkages, a new algorithm was developed to identify the different dyads of a mechanism. A dyad or class II group, is composed of two binary links connected by either a revolute (1) or a slider (0) pair with provision for attachment to other links by lower pair connectors located at the end of each link. There are five types of dyads: the D111, D101, D011, D001, and D010. The dyad analysis of a mechanism is predicated on the ability to construct the system from one or more of the five binary structure groups or class II groups. If the mechanism is complicated and several dyads are involved, the task of identifying these dyads by inspection could be difficult and time consuming for the user. This algorithm allows a complete automation of this task. This algorithm is based on the Dijkstra’s algorithm, for finding the shortest path in a graph, and it is used to develop a computer program, called KAMEL: Kinematic Analysis of MEchanical Linkages, and implemented on an IBM-PC PS/2 model 80. When compared to algorithmic methods, like the Newton-Raphson, the dyad method proved to be a very efficient one and requires as little as one tenth of the time needed by the method using Newton-Raphson algorithm. Moreover, the dyad method yields the exact solution of the position analysis and no initial estimates are needed to start the analysis. This method is also insensitive to the value of the step-size crank rotation, therefore, allowing a very accurate and fast solution of the mechanism at any position of the input link.

Position Analysis of Spatial Mechanisms

1984 ◽  
Vol 106 (2) ◽  
pp. 252-255 ◽  
Author(s):  
J. Llinares ◽  
A. Page
Keyword(s):  
Computational Algorithm ◽  
Matrix Notation ◽  
Position Analysis ◽  
Spatial Mechanisms ◽  
Lower Pair ◽  
Simple Equations

In this paper matrix notation is used to develop a computational algorithm for position analysis of spatial mechanisms having revolute (R) and prismatic (P) pairs. Since all lower pairs are equivalent to some combination of R and P pairs, the method works for spatial mechanisms containing any lower pair. By using the method, spatial mechanisms are describable by simple equations which are easily programmable.

Rapid Prototyping of Lower-Pair, Geared-Pair and Cam Mechanisms

2000 ◽  
Author(s):  
Thierry Laliberté ◽  
Clément M. Gosselin ◽  
Gabriel Côté
Keyword(s):  
Rapid Prototyping ◽  
Experimental Validation ◽  
Fused Deposition Modeling ◽  
3D Visualization ◽  
Fused Deposition ◽  
Lower Pair ◽  
Deposition Modeling ◽  
Kinematic Properties

Abstract In this paper, a framework for the rapid prototyping of lower-pair, geared-pair and cam mechanisms using a commercially available CAD package and a Fused Deposition Modeling (FDM) rapid prototyping machine is presented. A database of lower kinematic pairs (joints) is developed experimentally. Geared-pair and cam mechanisms are also developed. These mechanisms are then used in the design of the prototypes. Examples are presented in order to demonstrate the potential of this technique. Physical prototypes can be of great help in the design of mechanisms by allowing the 3D visualization of the mechanism as well as providing an experimental validation of the geometric and kinematic properties.

Electronic and optical properties of monolayer and bilayer graphene

2010 ◽  
Vol 368 (1932) ◽  
pp. 5445-5458 ◽  
Author(s):  
Y. H. Ho ◽  
J. Y. Wu ◽  
Y. H. Chiu ◽  
J. Wang ◽  
M. F. Lin
Keyword(s):  
Optical Properties ◽  
Bilayer Graphene ◽  
Landau Levels ◽  
Optical Measurements ◽  
Monolayer Graphene ◽  
Zero Field ◽  
Electronic And Optical Properties ◽  
Graphene Layers ◽  
Lower Pair ◽  
Dependent Absorption

The electronic and optical properties of monolayer and bilayer graphene are investigated to verify the effects of interlayer interactions and external magnetic field. Monolayer graphene exhibits linear bands in the low-energy region. Then the interlayer interactions in bilayers change these bands into two pairs of parabolic bands, where the lower pair is slightly overlapped and the occupied states are asymmetric with respect to the unoccupied ones. The characteristics of zero-field electronic structures are directly reflected in the Landau levels. In monolayer and bilayer graphene, these levels can be classified into one and two groups, respectively. With respect to the optical transitions between the Landau levels, bilayer graphene possesses much richer spectral features in comparison with monolayers, such as four kinds of absorption channels and double-peaked absorption lines. The explicit wave functions can further elucidate the frequency-dependent absorption rates and the complex optical selection rules. These numerical calculations would be useful in identifying the optical measurements on graphene layers.

scholarly journals Group Size as a Trade Off Between Fertility and Predation Risk: Implications for Social Evolution

2018 ◽  
Author(s):  
R.I.M. Dunbar ◽  
Padraig Mac Carron
Keyword(s):  
Cluster Analysis ◽  
Predation Risk ◽  
Group Size ◽  
Social Evolution ◽  
Female Fertility ◽  
Fertility Rates ◽  
Trade Off ◽  
Lower Pair ◽  
Increase Group Size ◽  
Do So

AbstractCluster analysis reveals a fractal pattern in the sizes of baboon groups, with peaks at ∼20, ∼40, ∼80 and ∼160. Although all baboon species individually exhibit this pattern, the two largest are mainly characteristic of the hamadryas and gelada. We suggest that these constitute three pairs of linear oscillators (20/40, 40/80 and 80/160), where in each case the higher value is set by limits on female fertility and the lower by predation risk. The lower pair of oscillators form an ESS in woodland baboons, with choice of oscillator being determined by local predation risk. Female fertility rates would naturally prevent baboons from achieving the highest oscillator with any regularity; nonetheless, hamadryas and gelada have been able to break through this fertility ‘glass ceiling’ and we suggest that they have been able to do so by using substructuring (based partly on using males as ‘hired guns’). This seems to have allowed them to increase group size significantly so as to occupy higher predation risk habitats (thereby creating the upper oscillator).

Design Considerations for an Articulated Leg-Wheel Locomotion Subsystem

2004 ◽  
Author(s):  
Seung Kook Jun ◽  
Venkat N. Krovi
Keyword(s):  
Sagittal Plane ◽  
Degree Of Freedom ◽  
Kinematic Synthesis ◽  
Ground Clearance ◽  
Uneven Terrain ◽  
Design Considerations ◽  
Serial Chain ◽  
Vehicle Systems ◽  
Lower Pair ◽  
Adequate Ground

In this paper, we examine and evaluate candidate articulated leg-wheel subsystem designs for use in vehicle systems with enhanced uneven-terrain locomotion capabilities. The leg-wheel subsystem designs under consideration consist of disk wheels attached to the chassis through an articulated linkage containing multiple lower-pair joints. Our emphasis is on creating a design that permits the greatest motion flexibility between the chassis and wheel while maintaining the smallest degree-of-freedom (d.o.f.) within the articulated chain. In particular, we focus our attention on achieving two goals: (i) obtaining adequate ground clearance by designing the desired/feasible motions of the wheel axle, relative to the chassis, using methods from kinematic synthesis; and (ii) reducing overall actuation requirements by a judicious mix of structural equilibration design and spring assist. We examine this process in the context of two candidate designs — a coupled-serial-chain configuration and four-bar-configuration — for the articulated-leg-wheel subsystem. The performance of planar variants of these designs, operating in the sagittal plane, is evaluated and representative results are presented to highlight the process.

Computational Local Mobility Analysis of Mechanisms With Higher Kinematic Pairs

2016 ◽  
Author(s):  
Andreas Müller
Keyword(s):  
Computational Algorithm ◽  
Computational Approach ◽  
Computational Method ◽  
Canonical Coordinates ◽  
Mobility Analysis ◽  
Local Mobility ◽  
Lower Pair ◽  
Order Constraints ◽  
Algebraic Operations ◽  
Higher Kinematic Pairs

The finite mobility of a mechanism is reflected by its configuration space (c-space), and the mobility analysis aims at determining this c-space. Crucial for the computational mobility analysis is an adequate formulation of the constraints. For lower pair linkages an analytic formulation is the product-of-exponential (POE) formula in terms of the screw systems of the lower pair joints. In other words, the screw coordinates of a lower pair joint serve as canonical coordinates on the corresponding motion subgroup. For such linkages, a computational approach to the local mobility analysis has been reported recently. The approach is applicable to general multi-loop linkages. Higher pairs do not generate motion subgroups so that their motion cannot be expressed in terms of screw coordinates. Hence their kinematics cannot be expressed in terms of a POE, and there is no efficient and generally applicable computational method for the mobility analysis. In this paper a formulation of higher-order constraints for mechanisms with higher pair joints is proposed making use of the result for lower pair linkages. The method is applicable to mechanisms where each fundamental loop comprises no more than one higher pair, which covers the majority of mechanisms. Based on this, a computational algorithm is introduced that allows mobility determination. As for lower pair linkages, this algorithm only requires simple algebraic operations.

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