Assessing Position Order in Rigid Body Guidance: An Intuitive Approach to Fixed Pivot Selection

2007 ◽  
Author(s):  
David H. Myszka ◽  
Andrew P. Murray ◽  
James P. Schmiedeler
Keyword(s):  
Rigid Body ◽  
Single Point ◽  
Entire Plane ◽  
Fixed Frame ◽  
Point Curve ◽  
Solution Methods ◽  
Pivot Selection ◽  
Line Passing ◽  
Pass Through ◽  
Degenerate Cases

This paper presents a new method for determining whether an RR dyad will pass through a set of finitely separated positions in order. Several established solution methods have been previously documented for this problem. This method utilizes only the displacement poles in the fixed frame to assess in an intuitive fashion whether a selected fixed pivot location will result in an ordered dyad solution. A line passing through the selected fixed pivot is rotated one-half revolution about the fixed pivot, in a manner similar to a propeller with infinitely long blades, to sweep the entire plane. Order is established by tracking the sequence of the displacement poles intersected by the rotating line. With four or five positions, fixed pivot locations corresponding to dyads having any specified order are readily found. Five-position problems can be directly evaluated to determine if any ordered solutions exist, and degenerate cases of four positions for which the set of fixed pivots corresponding to ordered dyads collapses to a single point on the center point curve can be identified.

Assessing Position Order in Rigid Body Guidance: An Intuitive Approach to Fixed Pivot Selection

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
David H. Myszka ◽  
Andrew P. Murray ◽  
James P. Schmiedeler
Keyword(s):  
Rigid Body ◽  
Single Point ◽  
New Method ◽  
Entire Plane ◽  
Fixed Frame ◽  
Center Point ◽  
Point Curve ◽  
Pivot Selection ◽  
Line Passing ◽  
Pass Through

Several established methods determine if an RR dyad will pass through a set of finitely separated positions in order. The new method presented herein utilizes only the displacement poles in the fixed frame to assess whether a selected fixed pivot location will yield an ordered dyad solution. A line passing through the selected fixed pivot is rotated one-half revolution about the fixed pivot, in a manner similar to a propeller with infinitely long blades, to sweep the entire plane. Order is established by tracking the sequence of displacement poles intersected. With four or five positions, fixed pivot locations corresponding to dyads having any specified order are readily found. Five-position problems can be directly evaluated to determine if any ordered solutions exist. Additionally, degenerate four-position cases for which the set of fixed pivots corresponding to ordered dyads that collapse to a single point on the center point curve can be identified.

Center-point Curves Through Six Arbitrary Points

1997 ◽  
Vol 119 (1) ◽  
pp. 36-39 ◽  
Author(s):  
A. P. Murray ◽  
J. Michael McCarthy
Keyword(s):  
Rigid Body ◽  
Kinematic Synthesis ◽  
Cubic Curve ◽  
Center Point ◽  
Point Curve ◽  
Non Linear ◽  
Pass Through ◽  
The Given

A circular cubic curve called a center-point curve is central to kinematic synthesis of a planar 4R linkage that moves a rigid body through four specified planar positions. In this paper, we show the set of circle-point curves is a non-linear subset of the set of circular cubics. In general, seven arbitrary points define a circular cubic curve; in contrast, we find that a center-point curve is defined by six arbitrary points. Furthermore, as many as three different center-point curves may pass through these six points. Having defined the curve without identifying any positions, we then show how to determine sets of four positions that generate the given center-point curve.

scholarly journals A Note on the Construction of a Set of Fundamental Circuits on a Surface of Genus p

1961 ◽  
Vol 4 (1) ◽  
pp. 13-21
Author(s):  
R. G. de Buda
Keyword(s):  
Single Point ◽  
Orientable Surface ◽  
Flat Region ◽  
Pass Through ◽  
The One

On an orientable surface of genus p, a set of 2p fundamental circuits can be selected which all pass through a single point A. After cutting along the 2p circuits, the surface can be unfolded into a flat region bounded by a 4p-gon so that: the set of vertices corresponds to the one point A; and the 2p pairs of edges to the 2p fundamental circuits; and the interior of the polygon to the remainder of the surface. If the edges of the polygon are directed, the 2 edges which correspond to one fundamental circuit will be directed in opposite sense, since the surface is orientable [1]. The sequence and direction of the edges is the same as the sequence of the fundamental circuits.

A Parameterization of the Central Axis Congruence Associated with Four Positions of a Rigid Body in Space

1993 ◽  
Vol 115 (3) ◽  
pp. 547-551 ◽  
Author(s):  
J. M. McCarthy
Keyword(s):  
Rigid Body ◽  
The Body ◽  
Central Axis ◽  
Spatial Mechanisms ◽  
Center Point ◽  
Point Curve ◽  
Screw Surface ◽  
Computer Based

Given four positions of a rigid body in space, there is a congruence of lines that can be used as the central axes of cylindric cranks to guide the body through the four positions. This “central axis congruence” is a generalization of the center point curve of planar kinematics. It is known that this congruence is identical to the screw congruence which arises in the study of complementary screw quadrilateral. It is less well-known that the screw congruence is the “screw surface” of the 4C linkage formed by the complementary screw quadrilateral, and it is this relationship that we use to obtain a parameterization for the screw congruence and in turn, the central axis congruence. This parameterization should facilitate the use of this congruence in computer based design of spatial mechanisms.

Theoretical analysis of "metabolic indices" of blood buffer system

1983 ◽  
Vol 244 (4) ◽  
pp. R492-R499
Author(s):  
T. Sato ◽  
N. Ikeda ◽  
H. Tsuruta ◽  
M. Shirataka
Keyword(s):  
Compartmental Model ◽  
Single Point ◽  
Empirical Finding ◽  
Hemoglobin Concentration ◽  
Least Square ◽  
Buffer System ◽  
Buffer Base ◽  
Acid Base Status ◽  
Pass Through ◽  
Metabolic Indices

The well-known base excess (BE) and buffer base (BB) curves of Siggaard-Andersen's nomogram are based on their empirical finding that the blood buffer lines in the pH-log PCO2 coordinates with the same BE (or BB) always pass through a single point irrespective of the hemoglobin concentration. We have analytically derived the BE and BB curves on the assumption of a two-compartmental model of blood buffer system comprised of plasma and red blood cells. These hyperbolic functions of BE and BB curves fitted the Siggaard-Andersen's observation very well. The simple formulas derived from the buffer equation with the parameters obtained on the least-square basis were shown to estimate “metabolic indices” of blood as accurately as the computer reading of the nomographic curves. These results seem to indicate that the buffer equation based on the two-compartmental model describes the acid-base status of blood satisfactorily, and that it can entirely replace the Siggaard-Andersen's nomogram.

A Variational Framework for Solution Method Developments in Structural Mechanics

1998 ◽  
Vol 65 (1) ◽  
pp. 242-249 ◽  
Author(s):  
K. C. Park ◽  
C. A. Felippa
Keyword(s):  
Rigid Body ◽  
Virtual Work ◽  
Full Rank ◽  
Structural Mechanics ◽  
Direct Construction ◽  
Parallel Solution ◽  
Variational Functional ◽  
Solution Algorithms ◽  
Variational Framework ◽  
Solution Methods

We present a variational framework for the development of partitioned solution algorithms in structural mechanics. This framework is obtained by decomposing the discrete virtual work of an assembled structure into that of partitioned substructures in terms of partitioned substructural deformations, substructural rigid-body displacements and interface forces on substructural partition boundaries. New aspects of the formulation are: the explicit use of substructural rigid-body mode amplitudes as independent variables and direct construction of rank-sufficient interface compatibility conditions. The resulting discrete variational functional is shown to be variation-ally complete, thus yielding a full-rank solution matrix. Four specializations of the present framework are discussed. Two of them have been successfully applied to parallel solution methods and to system identification. The potential of the two untested specializations is briefly discussed.

scholarly journals A Novel Tool to Enhance The Lubricant Efficiency On Induction Heat-Assisted Incremental Sheet Forming of Ti-6Al-4V Sheets

2022 ◽  
Author(s):  
Weining Li ◽  
Khamis Essa ◽  
Sheng Li
Keyword(s):  
Surface Quality ◽  
Single Point ◽  
Water Channel ◽  
Sheet Forming ◽  
Incremental Sheet Forming ◽  
Water Cooling ◽  
Geometric Accuracy ◽  
Molybdenum Disulphide ◽  
Roughness Analysis ◽  
Pass Through

Abstract For heat-assisted single point incremental sheet forming (SPIF) works of Ti-6Al-4V sheets, the use of lubricant has shown significant effects on surface quality and geometric accuracy at higher temperatures. Molybdenum disulphide (MoS2) is a common lubricant widely used in SPIF works, however, it usually indicates ineffective performance at high temperatures. This article has studied different lubricants of MoS2 lubricants and proposed a novel mixture of MoS2 to provide better surface quality and improve geometric accuracy. A forming tool with a ball-roller and water channel was designed to enable the MoS2 mixture to pass through the tool tip, allowing easy application of the lubricant on the localised area and reduce the thermal expansion on the ball-roller. Surface roughness analysis has revealed that the water-cooling MoS2 mixture performed well in reducing friction effects and achieved better geometric accuracy. Forming forces measurements, scanning electron microscope (SEM), energy dispersive X-ray Analysis (EDX) and micro-hardness tests also indicated that a higher strain hardening behaviour was detected for the water-cooling MoS2 mixture.

Confocal microscopy at the integrated microscopy resource for biomedical research (IMR) of the university of wisconsin

1988 ◽  
Vol 46 ◽  
pp. 92-93
Author(s):  
G. Schatten ◽  
S. Paddock ◽  
P. Cooke ◽  
J. Pawley
Keyword(s):  
Confocal Microscopy ◽  
Light Microscope ◽  
Laser Scanning ◽  
Single Point ◽  
Great Promise ◽  
Scanning Microscope ◽  
University Of Wisconsin ◽  
Pass Through ◽  
The University ◽  
Conventional Light Microscope

Confocal microscopy holds great promise for improved imaging of fluorescent or reflective biomedical specimens. The IMR is actively investigating the advantages and optimal usage of the Medical Research Council's Lasersharp laser - scanning confocal microscope and Tracor/Northern's Tandem Scanning Microscope, which benefits from the principles outlined by Petran et al. and Boyde.Quantitative evaluation of microscopic images has always been complicated by the effect of out-of-focus structures on the final image. These effects can be greatly reduced if the conventional light microscope is replaced by a scanning-confocal light microscope. In such an instrument two conditions are met: 1) only a single point of the sample is illuminated at any time and 2) this point on the sample is then imaged onto the pinhole at the entrance to the photodetector. Because little light from out-of-focus planes will pass through the pinhole, only in-focus data is recorded.

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.

Modeling and analytical methods for a mounting system with double stage isolation

2021 ◽  
pp. 095440702110632
Author(s):  
Yawei Zheng ◽  
Wen-Bin Shangguan ◽  
Yingzi Kang
Keyword(s):  
Free Vibration ◽  
Rigid Body ◽  
Motion Control ◽  
Three Dimensional ◽  
Vibration Equation ◽  
Proposed Model ◽  
Solution Methods ◽  
Rigid Body Modes ◽  
Simulation Results ◽  
Solutions Of Equations

A calculation method for obtaining the displacements and rigid body modes of a Powertrain Mounting System (PMS) with double stage isolation is proposed in this paper. Firstly, the PMS with double stage isolation is modeled as a 12 Degree of Freedoms (DOFs) model, which includes six DOFs for the powertrain and the subframe respectively. The mounts are simplified as a three-dimensional spring along each axis of its Local Mount Coordinate System (LMCS), which takes the non-linear relation of the force versus the displacement of each spring into account. Secondly, the quasi-static equilibrium equation and the free vibration equation as well as the forced vibration equation of the proposed model are derived and the solutions of equations are presented. Then, the calculation and solution methods are validated by the simulation results. The differences of rigid body modes and displacements of the powertrain between single and double stage isolation are estimated, which demonstrates that the proposed model is more accurate, especially when powertrain mounts are stiff. Also, the effect of locations for powertrain mounts on car body is investigated, which shows that is beneficial for motion control of powertrain.

Sign in / Sign up

Export Citation Format

Share Document