Singular Solutions in Burmester Theory

1973 ◽  
Vol 95 (2) ◽  
pp. 572-576 ◽  
Author(s):  
R. E. Kaufman
Keyword(s):  
Complex Number ◽  
Singular Solutions ◽  
Design Technique ◽  
Planar Mechanisms ◽  
Point Position ◽  
Proper Interpretation ◽  
General Synthesis ◽  
Number Development

A unified complex number development of four position planar finite position theory is presented. This formulation shows that Burmester circlepoint-centerpoint theory specializes to include slider points, concurrency points, poles, and point position reduction by proper interpretation of the trivial roots of the general synthesis equations. Thus a single design technique can be used for the multiposition synthesis of most pin or slider-jointed planar mechanisms. Four position function, path, or motion generating linkages can all be designed in this manner.

Coriolis acceleration analysis of planar mechanisms by complex-number algebra

1982 ◽  
Vol 17 (6) ◽  
pp. 405-414 ◽  
Author(s):  
George N Sandor ◽  
E Raghavacharyulu ◽  
Arthur G Erdman
Keyword(s):  
Complex Number ◽  
Planar Mechanisms ◽  
Coriolis Acceleration ◽  
Acceleration Analysis

Synthesis of Four-Link Space Mechanisms Via Extension of Point-Position-Reduction Technique

1971 ◽  
Vol 93 (1) ◽  
pp. 85-89 ◽  
Author(s):  
A. H. Soni ◽  
Matthew Huang
Keyword(s):  
Reduction Technique ◽  
Planar Mechanisms ◽  
Point Position ◽  
Position Synthesis ◽  
Space Mechanisms

The principle of point-position-reduction technique, which is used for position-synthesis of planar mechanisms, is extended to synthesize spherical four-link and spatial four-link RCCC mechanisms for four precision positions.

Order Rectification for Complex Number Based Burmester Curves

1991 ◽  
Vol 113 (3) ◽  
pp. 239-247 ◽  
Author(s):  
T. R. Chase ◽  
W. E. Fang
Keyword(s):  
Complex Number ◽  
Planar Mechanisms

A new solution to the order rectification problem for a driving dyad of planar mechanisms is presented. The method identifies sections of both Burmester curves where the driving link rotates in a single direction when passing through four precision positions in sequence. The new solution describes desirable regions of the curves in terms of the complex number parameters used to generate the curves, providing a complex number equivalent to available pole based order rectification procedures. The new solution is stated in a summary form that is readily codifiable. An example is presented. The theory underlying the new solution is then developed in detail.

Planar Circle-Point Equations for Finitely Separated and Double-Point Positions

1998 ◽  
Vol 123 (1) ◽  
pp. 157-160
Author(s):  
Hyoung Jun Kim ◽  
Raj S. Sodhi
Keyword(s):  
Rigid Body ◽  
Double Point ◽  
Rigid Body Motion ◽  
Body Motion ◽  
New Method ◽  
Planar Mechanisms ◽  
Point Position ◽  
Point Curve ◽  
New Form ◽  
Position Problem

The rigid body motion is studied for a combination of finitely and infinitesimally separated positions in planar kinematics. A general new method is developed for determining the locations of points in a rigid body moving through finitely and infinitesimally separated positions. These points would satisfy the constraints of the crank links for planar mechanisms. A new form of the circle-point curve equations is derived for the double-point position problem and also for the finitely separated position problem in planar kinematics.

New Complex-Number Form of the Cubic of Stationary Curvature in a Computer-Oriented Treatment of Planar Path-Curvature Theory for Higher-Pair Rolling Contact

1982 ◽  
Vol 104 (1) ◽  
pp. 233-238 ◽  
Author(s):  
G. N. Sandor ◽  
A. G. Erdman ◽  
L. Hunt ◽  
E. Raghavacharyulu
Keyword(s):  
Complex Number ◽  
Rate Of Change ◽  
Rolling Contact ◽  
Planar Mechanisms ◽  
Digital Computation ◽  
Complex Arithmetic ◽  
Moving Plane ◽  
Curvature Theory ◽  
Path Curvature ◽  
Number Form

New complex number forms of the Euler-Savary Equation (ESE) for higher-pair rolling contact planar mechanisms were derived in a former paper by the authors. The present work, based on the former, deals with the derivation of the cubic of stationary curvature (CSC) in complex-vector form, suitable for digital computation. The CSC or Burmester’s circlepoint curve and its conjugate, the centerpoint curve for four infinitesimally close positions of the moving plane requires taking into account not only the curvature but also the rate of change of curvature of the rolling centrodes in the immediate vicinity of the position considered. The analytical procedure based on the theory developed in the present paper, when programmed for digital computation using complex arithmetic, takes care of the algebraic signs automatically, without the need for observing traditional sign conventions. The analysis is applicable to both higher-pair and lower-pair planar mechanisms. An example using the complex-number approach illustrates this.

New Complex-Number Forms of the Euler-Savary Equation in a Computer-Oriented Treatment of Planar Path-Curvature Theory for Higher-Pair Rolling Contact

1982 ◽  
Vol 104 (1) ◽  
pp. 227-232 ◽  
Author(s):  
G. N. Sandor ◽  
A. G. Erdman ◽  
L. Hunt ◽  
E. Raghavacharyulu
Keyword(s):  
Complex Number ◽  
Rolling Contact ◽  
Radius Of Curvature ◽  
Planar Mechanisms ◽  
Kinematic Synthesis ◽  
Synthesis Of Mechanisms ◽  
Curvature Theory ◽  
Path Curvature ◽  
Planar Linkages ◽  
Contact Mechanism

It is well known from the theory of Kinematic Synthesis of planar mechanisms that the Euler-Savary Equation (ESE) gives the radius of curvature and the center of curvature of the path traced by a point in a planar rolling-contact mechanism. It can also be applied in planar linkages for which equivalent roll-curve mechanisms can be found. Typical example: the curvature of the coupler curve of a four-bar mechanism. Early works in the synthesis of mechanisms concerned themselves with deriving the ESE by means of combined graphical and algebraic techniques, using certain sign conventions. These sign conventions often become sources of error. In this paper new complex-number forms of the Euler-Savary Equation are derived and are presented in a computer-oriented format. The results are useful in the application of path-curvature theory to higher-pair rolling contact mechanisms, such as cams, gears, etc., as well as linkages, once the key parameters of an equivalent rolling-contact mechanism are known. The complex-number technique has the advantage of eliminating the need for the traditional sign conventions and is suitable for digital computation. An example is presented to illustrate this.

Triad Synthesis for up to Five Design Positions With Application to the Design of Arbitrary Planar Mechanisms

1987 ◽  
Vol 109 (4) ◽  
pp. 426-434 ◽  
Author(s):  
T. R. Chase ◽  
A. G. Erdman ◽  
D. R. Riley
Keyword(s):  
Complex Number ◽  
Path Generation ◽  
Dimensional Synthesis ◽  
Planar Mechanisms ◽  
Relative Precision ◽  
Synthesis Techniques ◽  
New Synthesis ◽  
Actual Mechanism ◽  
Synthesis Tool

A new synthesis tool, the triad, is introduced to enable simplified synthesis of very complex planar mechanisms. The triad is a connected string of three vectors representing jointed rigid links of an actual mechanism. The triad is used as a tool to model an original mechanism topology with a set of simpler components. Each triad is then used to generate a set of “relative precision positions” which, in turn, enables the dimensional synthesis of each triad with well-established motion and path generation techniques for simple four-bar linkages. Two independent derivations of the relative precision positions are provided. All common triad geometries amenable to simple dyad synthesis techniques are presented. The triad geometries summarized here may be applied to two, three, four, and five precision position problems using graphical, algebraic, or complex number formulations of Burmester theory. Examples are provided.

A Constrained Search Technique for Motion Generator Pivot Location

1987 ◽  
Author(s):  
T. J. Lawley ◽  
R. V. Nambiar ◽  
J. K. Nisbett ◽  
S. Prince ◽  
H. Zarefar
Keyword(s):  
Computer Program ◽  
Complex Number ◽  
Random Search ◽  
Search Technique ◽  
Planar Mechanisms ◽  
Automobile Suspension ◽  
Pass Through ◽  
Motion Generator

Abstract Burmester’s solution to the problem of guiding a body through four precision points has been extended to find planar mechanisms that have their pivots located inside prescribed regions. The complex number formulation has been used to generate the Burmester curves. A random search technique was developed to choose a new set of precision points that lie within user specified limits, in order to find a set of curves that pass through the desired regions. A computer program was written to generate Burmester curves that lie within the desired regions, while maintaining a coupler motion within satisfactory limits. An automobile suspension linkage was successfully designed using this program.

Survival of Short and Ultra-Short Locking-Taper Implants Supporting Single Crowns in the Posterior Mandible: A 3-Year Retrospective Study

2020 ◽  
Vol 46 (4) ◽  
pp. 396-406 ◽  
Author(s):  
Giorgio Lombardo ◽  
Annarita Signoriello ◽  
Miguel Simancas-Pallares ◽  
Mauro Marincola ◽  
Pier Francesco Nocini
Keyword(s):  
Retrospective Study ◽  
Bone Loss ◽  
Contact Point ◽  
Implant Survival ◽  
Point Position ◽  
Crestal Bone Loss ◽  
Short Implants ◽  
Single Crown ◽  
Bone To Implant Contact ◽  
Single Crowns

The purpose of this retrospective study was to determine survival and peri-implant marginal bone loss of short and ultra-short implants placed in the posterior mandible. A total of 98 patients received 201 locking-taper implants between January 2014 and January 2015. Implants were placed with a 2-stage approach and restored with single crowns. Clinical and radiographic examinations were performed at 3-year recall appointments. At that time, the proportion of implant survival by length, and variations of crestal bone levels (mean crestal bone loss and mean apical shift of the “first bone-to-implant contact point” position) were assessed. Significance level was set at 0.05. The total number of implants examined 36 months after loading included: 71 implants, 8.0 mm in length; 82 implants, 6.0 mm in length; and 48 implants, 5.0 mm in length. Five implants failed. The overall proportion of survival was 97.51%, with 98.59% for the 8.0-mm implants, 97.56% for the 6.0-mm implants, and 95.83% for the 5.0-mm implants. No statistically significant differences were found among the groups regarding implant survival (P = .73), mean crestal bone loss (P = .31), or mean apical shift of the “first bone-to-implant contact point” position (P = .36). Single-crown short and ultra-short implants may offer predictable outcomes in the atrophic posterior mandibular regions, though further investigations with longer follow-up evaluations are necessary to validate our results.

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