Some Special Cases of the Burmester Problem for Four and Five Poses

2005 ◽  
Author(s):  
Jorge Angeles ◽  
Shaoping Bai
Keyword(s):  
Synthesis Method ◽  
Geometric Parameters ◽  
Special Treatment ◽  
End Point ◽  
Displacement Vectors ◽  
Special Cases ◽  
Common Intersection ◽  
Four Bar Linkage ◽  
Special Case

The Burmester problem aims at finding the geometric parameters of a planar four-bar linkage for a prescribed set of finitely separated poses. The synthesis related to the Burmester problem deals with both revolute-revolute (RR) and prismatic-revolute (PR) dyads. A PR dyad is a special case of RR dyad, i.e., a dyad with one end-point at infinity. The special nature of PR dyads warrants a special treatment, outside of the general methods of four-bar linkage synthesis, which target mainly RR dyads. In this paper, we study the synthesis of planar four-bar linkages addressing the problem of the determination of PR dyads. The conditions for the presence of PR dyads with the prescribed poses are derived. A synthesis method is developed by resorting to the parallelism condition of the displacement vectors of the circle points of PR dyads. We show that the “circle” point of a PR dyad can be determined as one common intersection of three or four circles, depending on whether four or, correspondingly, five poses are prescribed.

The Synthesis of Dyads With One Prismatic Joint

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Chao Chen ◽  
Shaoping Bai ◽  
Jorge Angeles
Keyword(s):  
Geometric Parameters ◽  
Special Treatment ◽  
Prismatic Joint ◽  
Invariant Formulation ◽  
Underlying Geometry ◽  
Joint Center ◽  
Four Bar Linkage ◽  
Special Case ◽  
Linkage Synthesis

The classic Burmester problem aims at finding the geometric parameters of a planar four-bar linkage for a prescribed set of finitely separated poses. The synthesis related to the Burmester problem deals with revolute-revolute (RR), prismatic-revolute (PR), and revolute-prismatic (RP) dyads. A PR dyad is a special case of the RR dyad, namely, a dyad of this kind with its fixed joint center at infinity; a similar interpretation applies to the RP dyad. The special nature of dyads with one P joint warrants a special treatment, outside of the general methods of four-bar linkage synthesis, which target mainly RR dyads. In proposing robust computational means to synthesize PR and RP dyads, we adopt an invariant formulation, which, additionally, sheds light on the underlying geometry.

Analytical Techniques for the Optimisation of Rocket Trajectories

1963 ◽  
Vol 14 (2) ◽  
pp. 105-124 ◽  
Author(s):  
Derek F. Lawden
Keyword(s):  
Gravitational Field ◽  
Artificial Satellite ◽  
Analytical Techniques ◽  
Present Position ◽  
Mayer Problem ◽  
Special Cases ◽  
Minimum Expenditure ◽  
Law Of Attraction ◽  
Special Case

SummaryThe development during the last two decades of analytical techniques for the solution of problems relating to the optimisation of rocket trajectories is outlined and the present position in this field of research is summarised. It is shown that the determination of optimal trajectories in a general gravitational field can be expressed as a Mayer problem from the calculus of variations. The known solution to such a problem is stated and applied, first to the special case of the launching of an artificial satellite into a circular orbit with minimum expenditure of propellant and, secondly, to the general astronautical problem of the economical transfer of a rocket between two terminals in a gravitational field. The special cases when the field is uniform and when it obeys an inverse square law of attraction to a point are then considered, and the paper concludes with some remarks concerning areas in which further investigations are necessary.

scholarly journals Estimation of the residual resource of wooden structures by changing geometric parameters of the cross-section

2021 ◽  
Vol 244 ◽  
pp. 04010
Author(s):  
Dmitry Korolkov ◽  
Marina Gravit ◽  
Maxim Aleksandrovskiy
Keyword(s):  
Service Life ◽  
General Formula ◽  
Cross Section ◽  
Axial Force ◽  
Rate Of Change ◽  
Geometric Parameters ◽  
Advantages And Disadvantages ◽  
Special Cases ◽  
Wooden Structures

In this article, the authors propose a method for assessing the residual resource by changing the geometric parameters of wooden structures. A general formula for estimating the maximum service life is presented. Then a number of special cases are considered when calculating the ultimate service life for the first group of limiting states. As a result, formulas were derived for calculating the ultimate service life for various design cases: centrally tensioned, centrally compressed, bending members, members subject to an axial force with bending. The author considered the determination of the rate of change in geometric parameters at the macrolevel (visually observed changes) and microscopic (microcracks, breaks of bonds between atoms). Formulas for determining the rate of change of geometric parameters at the macro and micro levels are proposed. The advantages and disadvantages of this method are presented. The scope of its application is indicated.

A Method for Adjustable Planar and Spherical Four-Bar Linkage Synthesis

2004 ◽  
Vol 127 (3) ◽  
pp. 456-463 ◽  
Author(s):  
Boyang Hong ◽  
Arthur G. Erdman
Keyword(s):  
Synthesis Method ◽  
New Method ◽  
Spherical Form ◽  
Numerical Example ◽  
Input And Output ◽  
Special Cases ◽  
Position Synthesis ◽  
Four Bar Linkage ◽  
Linkage Synthesis

This paper describes a new method to synthesize adjustable four-bar linkages, both in planar and spherical form. This method uses fixed ground pivots and an adjustable length for input and output links. A new application of Burmester curves for adjustable linkages is introduced, and a numerical example is discussed. This paper also compares a conventional synthesis method (nonadjustable linkage) to the new method. Nonadjustable four-bar linkages provide limited solutions for five-position synthesis. Adjustable linkages generate one infinity of solution choices. This paper also shows that the nonadjustable solutions are special cases of adjustable solutions. This new method can be extended to six position synthesis, with adjustable ground pivots locations.

A Robust Solution of the Spherical Burmester Problem

2010 ◽  
Author(s):  
Jorge Angeles ◽  
Shaoping Bai
Keyword(s):  
Solution Method ◽  
Synthesis Method ◽  
Robust Solution ◽  
Equation Solving ◽  
Prismatic Joints ◽  
Four Bar Linkage ◽  
Special Case ◽  
Robust Synthesis ◽  
Linkage Synthesis

The problem of spherical four-bar linkage synthesis is revisited in this paper. The work is aimed at developing a robust synthesis method by taking into account both the formulation and the solution method. In addition, the synthesis of linkages with spherical prismatic joints is considered by treating them as a special case of the linkages under study. A two-step synthesis method is developed, which sequentially deals with equation-solving by a semigraphical approach and branching-detection. Examples are included to demonstrate the proposed method.

scholarly journals Estimation of the residual resource of wooden structures by the changes of the cross section geometric parameters

2021 ◽  
Vol 18 (2) ◽  
pp. 49-56
Author(s):  
D. I. Korolkov ◽  
Keyword(s):  
General Formula ◽  
Cross Section ◽  
Rate Of Change ◽  
Geometric Parameters ◽  
Advantages And Disadvantages ◽  
Micro Cracks ◽  
Special Cases ◽  
Micro Level ◽  
Wooden Structures

In this article, the author proposes a method for assessing the residual resource of wooden structures by changes taking place in their geometric parameters. A general formula for estimating the service limit of the wooden structures is presented. Then, a number of special cases are considered when calculating the service limit for the first group of limiting states. As a result, formulas have been derived for calculating the service limit for various design cases, namely, centrally tensioned, centrally compressed members, members under bending, members subjected to the axial force with bending. The author considers the determination of the rate of geometric parameters change at the macro-level (visually observed changes) and micro-level (micro-cracks, breaks of bonds between atoms). Formulas for determining the rate of change of geometric parameters at the macro and micro levels are proposed. The advantages and disadvantages of this method are highlighted, and the scope of its application is indicated.

Determination of the phase structure of polymerblends by electron microscopy

1978 ◽  
Vol 36 (1) ◽  
pp. 492-493
Author(s):  
Dr. G. Kaemof
Keyword(s):  
Screw Extruder ◽  
Electron Microscopic ◽  
Thin Sections ◽  
Single Screw Extruder ◽  
Transmission Electron ◽  
The Matrix ◽  
Twin Screw ◽  
Special Case ◽  
Microscopic Investigations

A mixture of polycarbonate (PC) and styrene-acrylonitrile-copolymer (SAN) represents a very good example for the efficiency of electron microscopic investigations concerning the determination of optimum production procedures for high grade product properties.The following parameters have been varied:components of charge (PC : SAN 50 : 50, 60 : 40, 70 : 30), kind of compounding machine (single screw extruder, twin screw extruder, discontinuous kneader), mass-temperature (lowest and highest possible temperature).The transmission electron microscopic investigations (TEM) were carried out on ultra thin sections, the PC-phase of which was selectively etched by triethylamine.The phase transition (matrix to disperse phase) does not occur - as might be expected - at a PC to SAN ratio of 50 : 50, but at a ratio of 65 : 35. Our results show that the matrix is preferably formed by the components with the lower melting viscosity (in this special case SAN), even at concentrations of less than 50 %.

scholarly journals KD determination from time-resolved experiments on live cells with LigandTracer and reconciliation with end-point flow cytometry measurements

2021 ◽  
Author(s):  
Diana Spiegelberg ◽  
Jonas Stenberg ◽  
Pascale Richalet ◽  
Marc Vanhove
Keyword(s):  
Flow Cytometry ◽  
Live Cells ◽  
Time Resolved ◽  
Surface Receptors ◽  
Full Characterization ◽  
End Point ◽  
Titration Curves ◽  
Kinetics Of

AbstractDesign of next-generation therapeutics comes with new challenges and emulates technology and methods to meet them. Characterizing the binding of either natural ligands or therapeutic proteins to cell-surface receptors, for which relevant recombinant versions may not exist, represents one of these challenges. Here we report the characterization of the interaction of five different antibody therapeutics (Trastuzumab, Rituximab, Panitumumab, Pertuzumab, and Cetuximab) with their cognate target receptors using LigandTracer. The method offers the advantage of being performed on live cells, alleviating the need for a recombinant source of the receptor. Furthermore, time-resolved measurements, in addition to allowing the determination of the affinity of the studied drug to its target, give access to the binding kinetics thereby providing a full characterization of the system. In this study, we also compared time-resolved LigandTracer data with end-point KD determination from flow cytometry experiments and hypothesize that discrepancies between these two approaches, when they exist, generally come from flow cytometry titration curves being acquired prior to full equilibration of the system. Our data, however, show that knowledge of the kinetics of the interaction allows to reconcile the data obtained by flow cytometry and LigandTracer and demonstrate the complementarity of these two methods.

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