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.

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.

A Study of the Duality Between Planar Kinematics and Statics

2005 ◽  
Vol 128 (3) ◽  
pp. 587-598 ◽  
Author(s):  
Offer Shai ◽  
Gordon R. Pennock
Keyword(s):  
Unique Point ◽  
Planar Mechanisms ◽  
Unique Line ◽  
Original Contribution ◽  
Basic Concepts ◽  
Instantaneous Center ◽  
Force Variable ◽  
Pass Through ◽  
Insight Into ◽  
General Perspective

This paper provides geometric insight into the correlation between basic concepts underlying the kinematics of planar mechanisms and the statics of simple trusses. The implication of this correlation, referred to here as duality, is that the science of kinematics can be utilized in a systematic manner to yield insight into statics, and vice versa. The paper begins by introducing a unique line, referred to as the equimomental line, which exists for two arbitrary coplanar forces. This line, where the moments caused by the two forces at each point on the line are equal, is used to define the direction of a face force which is a force variable acting in a face of a truss. The dual concept of an equimomental line in kinematics is the instantaneous center of zero velocity (or instant center) and the paper presents two theorems based on the duality between equimomental lines and instant centers. The first theorem, referred to as the equimomental line theorem, states that the three equimomental lines defined by three coplanar forces must intersect at a unique point. The second theorem states that the equimomental line for two coplanar forces acting on a truss, with two degrees of indeterminacy, must pass through a unique point. The paper then presents the dual Kennedy theorem for statics which is analogous to the well-known Aronhold-Kennedy theorem in kinematics. This theorem is believed to be an original contribution and provides a general perspective of the importance of the duality between the kinematics of mechanisms and the statics of trusses. Finally, the paper presents examples to demonstrate how this duality provides geometric insight into a simple truss and a planar linkage. The concepts are used to identify special configurations where the truss is not stable and where the linkage loses mobility (i.e., dead-center positions).

The Duality Between Planar Kinematics and Statics

2005 ◽  
Author(s):  
Offer Shai ◽  
Gordon R. Pennock
Keyword(s):  
Mechanical Systems ◽  
Unique Point ◽  
Singular Configurations ◽  
New Concepts ◽  
Basic Concepts ◽  
Instantaneous Center ◽  
Pass Through ◽  
Planar Linkages ◽  
Insight Into ◽  
General Perspective

This paper shows that there is a correlation between basic concepts underlying the kinematics of mechanisms and the statics of trusses. The implication of this correlation, referred to here as duality, is that the science of kinematics can be utilized in a systematic manner to yield insight into the statics of mechanical systems. The paper begins by proving the existence of a unique line (referred to as the equimomental line) where the moments, at each point on this line, caused by two arbitrary co-planar forces are equal. The dual concept in kinematics is the instantaneous center of zero velocity and two theorems are presented based on the duality between equimomental lines and instantaneous centers. The first theorem states that the three equimomental lines defined by three co-planar forces must intersect at a unique point. The second theorem states that the equimomental line for two co-planar forces acting in a trusss with two degrees of indeterminacy must pass through a unique point. The paper presents several practical examples to demonstrate how the duality between kinematics and statics provides a better understanding of planar linkages and trusses. The new concepts are used to identify the singular configurations of linkages and the configurations of determinate trusses where they are not rigid. Finally, the paper takes advantage of some important relationships between linkages and trusses to provide a general perspective of the duality between the kinematics of mechanisms and the statics of trusses.

scholarly journals A generalized view on normal moveout

Geophysics ◽  
2017 ◽  
Vol 82 (5) ◽  
pp. V335-V349 ◽  
Author(s):  
Benjamin Schwarz ◽  
Dirk Gajewski
Keyword(s):  
Seismic Events ◽  
Velocity Analysis ◽  
The Past ◽  
Dual Representations ◽  
Optical Projection ◽  
Passive Seismic ◽  
Common Reflection Surface ◽  
The Common ◽  
Ray Geometry ◽  
Insight Into

Although in the past, in the context of stacking, traveltime moveout was only formulated in individual common-midpoint (CMP) gathers, multiparameter stacking uses normal moveout (NMO) approximations that span several neighboring CMPs. Multiparameter expressions such as the common reflection surface (CRS) or multifocusing are parameterized in terms of local slopes and curvatures of emerging wavefronts rather than effective velocities, which makes these approaches appear conceptually different from conventional velocity analysis. As a consequence, the unifying nature of multiparameter NMO is still not well-appreciated. In addition, CRS and multifocusing show distinctly different behavior in that they respond differently to the overburden heterogeneity and curvature of the target interface, and they either are or are not susceptible to moveout stretch. In our work, we seek to demystify the wavefront picture by demonstrating that the conventional and multidimensional NMO operators can conveniently be derived from the same auxiliary straight-ray geometry, either representing the optical projection or formulated in an effective replacement medium. Following the early work of de Bazelaire, we suggest a simple transformation between both domains and introduce generalized dual representations of the hyperbolic CRS, multifocusing, and the two recently introduced double-square-root expressions implicit CRS and nonhyperbolic CRS. In addition, we evaluate a generalized finite-offset NMO expression that can likewise be applied to active-source diffraction data and passive seismic events. Synthetic examples suggest unification, conveniently explain the origin of moveout stretch, and indicate that the joint use of different NMO approximations offers new insight into the character and origin of different wavefield components.

Evaluating managerial efficiency of petrochemical firms in Saudi Arabia

2017 ◽  
Vol 24 (1) ◽  
pp. 244-256
Author(s):  
Mohammad Hanif Akhtar ◽  
Muhammad Asif
Keyword(s):  
Saudi Arabia ◽  
Design Methodology ◽  
Economies Of Scale ◽  
Data Envelopment ◽  
Kingdom Of Saudi Arabia ◽  
Content Type ◽  
Managerial Efficiency ◽  
Original Contribution ◽  
Practical Implications ◽  
Insight Into

Purpose The purpose of this paper is to examine managerial efficiency of the whole population of petrochemical firms in the Kingdom of Saudi Arabia (KSA). It also identifies the root causes of inefficiencies and proposes measures to overcome these. Design/methodology/approach The paper uses the data envelopment analysis approach to measure the managerial efficiency in context of various returns-to-scales. To glean further insights into the sources of inefficiency, the study investigates the extent of utilization of resources by comparing target inputs vis-à-vis the actual inputs used. This provides the authors information about the degree of underutilization of resources as well as an insight into the sources of inefficiency, e.g., those stemming from the managerial or scale of operations. Findings The findings reveal a great amount of inefficiencies in Saudi petrochemical sector. These inefficiencies arise from both the underutilization of resources as well as the inability of petrochemical firms to run their operations at optimal scales. Practical implications The findings of the study allude toward measures that managers might adopt to overcome the issues of inefficiency. They ought to ensure better utilization of resources by running operations of the firms at optimal scales of production. The firms operating under the sub-optimum scales of operations need to revisit their marketing and production strategies. These might take up the form of boosting marketing efforts to win more orders from customers and increasing production volumes that could allow these firms to take advantage of economies of scale. Originality/value This paper is a first attempt to measure efficiency of petrochemical sector in KSA which stands as the key contributor to the national exchequer. Since the study consists of the whole population of petrochemical firms in KSA, it measures the “true” managerial efficiency of petrochemical firms in the sector. Further, being a pioneer study on managerial efficiency of petrochemical sector, it extends original contribution to the literature on efficiency of firms, combined with rich insights into sources of inefficiencies.

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.

scholarly journals A new graphical technique for acceleration analysis of four bar mechanisms using the instantaneous center of zero acceleration

2021 ◽  
Vol 3 (3) ◽  
Author(s):  
Nadim Diab
Keyword(s):  
Angular Acceleration ◽  
Graphical Technique ◽  
Acceleration Analysis ◽  
Instantaneous Center

AbstractIn this work, a new graphical technique is furnished for acceleration analysis of four bar mechanisms through locating the instantaneous center of zero acceleration $$IC_{a}$$ I C a of the coupler link. First, the paper observes the coupler’s $$IC_{a}$$ I C a locus and then proceeds with a series of graphical constructions that eventually lead into locating the $$IC_{a}$$ I C a and obtaining the linear/angular accelerations of the coupler and follower (or slider) links. Based on the proposed graphical technique, the ease of acceleration analysis for four-bar mechanisms with varying driver’s angular acceleration is demonstrated. Simultaneously, the inflection circle of the coupler curve is constructed without the need to apply Euler-Savary equations. With fewer constructions than classical graphical techniques, the robustness and simplicity of the proposed method are demonstrated by performing acceleration analysis of a slider-crank (RRRP) and a planar quadrilateral linkage (RRRR).

Coupler Cognates for the Double Flier Eight-Bar Linkage

2005 ◽  
Vol 127 (6) ◽  
pp. 1145-1151 ◽  
Author(s):  
Gordon R. Pennock ◽  
Nihar N. Raje
Keyword(s):  
Analytical Techniques ◽  
Input Output ◽  
Straightforward Manner ◽  
Graphical Approach ◽  
Locus Equation ◽  
Original Contribution ◽  
Kinematic Inversion ◽  
Angular Velocities ◽  
Graphical Technique ◽  
High Degree

This paper presents a graphical technique to construct the coupler cognate linkages for the double flier eight-bar linkage. The technique is based on the skew pantograph construction which converts the double flier linkage into a second eight-bar linkage by applying the concepts of stretch rotation and kinematic inversion. Since a stretch-rotation operation preserves the angular velocities of corresponding links of the two linkages then the second linkage has the same input-output motion as the original double flier linkage. Another stretch rotation is performed on the intermediate eight-bar linkage and a third eight-bar linkage, which duplicates the motion of the coupler link of the original linkage, is obtained. This graphical approach, to investigating coupler cognates, is believed to be an original contribution to the study of cognate linkages. The technique can be applied in a straightforward manner, requiring few constructions, and offers significant advantages over well-known analytical techniques which use the locus equation. For the double flier eight-bar linkage, the locus equation is of a high degree and the coefficients can only be obtained from a very laborious procedure. This paper shows the existence of two coupler cognates for each of the two floating binary links of the double flier eight-bar linkage that are connected to the ternary link which is pinned to ground.

scholarly journals Cellular sensing of micron-scale curvature: a frontier in understanding the microenvironment

Open Biology ◽  
2019 ◽  
Vol 9 (10) ◽  
pp. 190155 ◽  
Author(s):  
Richard K. Assoian ◽  
Nathan D. Bade ◽  
Caroline V. Cameron ◽  
Kathleen J. Stebe
Keyword(s):  
Molecular Mechanisms ◽  
Radius Of Curvature ◽  
Valuable Insight ◽  
Glass Plastic ◽  
Cell Behaviour ◽  
Flat Surfaces ◽  
Biological Studies ◽  
And Function ◽  
Insight Into

The vast majority of cell biological studies examine function and molecular mechanisms using cells on flat surfaces: glass, plastic and more recently elastomeric polymers. While these studies have provided a wealth of valuable insight, they fail to consider that most biologically occurring surfaces are curved, with a radius of curvature roughly corresponding to the length scale of cells themselves. Here, we review recent studies showing that cells detect and respond to these curvature cues by adjusting and re-orienting their cell bodies, actin fibres and nuclei as well as by changing their transcriptional programme. Modelling substratum curvature has the potential to provide fundamental new insight into cell behaviour and function in vivo .

Building franchisee trust in their franchisor: insights from the franchise sector

2016 ◽  
Vol 19 (1) ◽  
pp. 65-83 ◽  
Author(s):  
Anthony Richard Grace ◽  
Lorelle Frazer ◽  
Scott K. Weaven ◽  
Rajiv P Dant
Keyword(s):  
Second Phase ◽  
Structured Interviews ◽  
Content Type ◽  
Franchise System ◽  
Team Culture ◽  
Original Contribution ◽  
Practical Model ◽  
Practical Implications ◽  
Insight Into ◽  
Practical Recommendations

Purpose – The purpose of this research is to identify the critical determinants of a franchisee’s trust in their franchisor. Design/methodology/approach – A qualitative approach was used, and 30 interviews were conducted with franchising participants. The first phase of the research consisted of exploratory interviews with franchising experts (franchise lawyers, accountants, consultants, mediators and bankers), and the second phase consisted of semi-structured interviews with franchisees and franchisors across two franchise systems. Findings – The research revealed five critical determinants of a franchisee’s trust in their franchisor: franchisee’s engagement in the system, franchisee’s confidence in the system, franchisee’s perception of a strong team culture, franchisee’s perception of franchisor competence and franchisee’s perception of franchisor character. Practical implications – The research provides insight into how the aforementioned components can be developed within a franchise system to build franchisee trust. The paper also concludes with four practical recommendations that can be integrated within a franchise system to increase levels of franchisee trust. Originality/value – This research builds on prior research into franchisee trust, providing an original contribution to the literature through the development of a practical model, showcasing critical determinants of a franchisee’s trust in their franchisor.

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