The Optimization of Dimensions of an Adjustable Mechanism for a Packaging Machine

1989 ◽  
Vol 203 (1) ◽  
pp. 37-40 ◽  
Author(s):  
A Daadbin ◽  
K S H Sadek
Keyword(s):  
Rigid Body ◽  
Complex Mechanism ◽  
Uniform Velocity ◽  
Packaging Machine ◽  
Minimum Number ◽  
Adjustable Mechanism ◽  
Spatial Linkages ◽  
Mechanical Devices ◽  
Cam Systems

Mechanisms form the basic geometrical elements of many mechanical devices including automatic packaging machinery, typewriters, textile and printing machinery, and others. A mechanism typically is designed to create a desired motion of a rigid body relative to a reference member by the help of gears, cam systems or spatial linkages. In flow pack machines a tube of wrapper containing the products moves with a uniform velocity, while the reciprocating heads move forward and backwards sealing different products. In an existing machine, these motions are produced by a rather complex mechanism involving cams and adjustable links. The paper suggests replacing these cams by a suitable quick-return mechanism with a minimum number of adjustable links. The dimensions of this mechanism are optimized such that the motions produced are as near as possible to those obtained by the original cam mechanisms. The simplification can result in reduction in the mass of different components and existing forces in the mechanism.

On the Minimum Number of Counterweights for Multi-Loop Spatial Linkages

1985 ◽  
Vol 107 (4) ◽  
pp. 526-528
Author(s):  
Q.-X. Zhang ◽  
N.-X. Chen
Keyword(s):  
Minimum Number ◽  
Spatial Linkages

This paper offers extensions to the force-balancing theory and the techniques of spatial linkages given in [9-12]. It incorporates another technique for determining the minimum number of counterweights needed for a full balance and discusses the minimum number of counterweights without attachment to any common floating link of loops. Some examples are given to illustrate the application of these results.

Incompletely Specified Displacements: Geometry and Spatial Linkage Synthesis

1973 ◽  
Vol 95 (2) ◽  
pp. 603-611 ◽  
Author(s):  
Lung-Wen Tsai ◽  
Bernard Roth
Keyword(s):  
Rigid Body ◽  
Screw Axis ◽  
Numerical Examples ◽  
Spatial Linkages ◽  
Free Parameters ◽  
Analytical Expressions ◽  
Linkage Synthesis

The screw axis geometry associated with displacements of points and lines is studied. Analytical expressions are developed for rigid body screw displacements which have one or more free parameters. It is shown how to apply these results to the synthesis of spatial linkages. The theory is illustrated by numerical examples in which Cylindric-Cylindric cranks are designed to guide two points in a rigid body through five and then nine specified positions.

Design Rules for Selecting and Designing Compliant Mechanisms for Rigid-Body Replacement Synthesis

2000 ◽  
Author(s):  
Michael D. Berglund ◽  
Spencer P. Magleby ◽  
Larry L. Howell
Keyword(s):  
Rigid Body ◽  
Compliant Mechanisms ◽  
Rational Method ◽  
Design Concept ◽  
Design Features ◽  
Design Problems ◽  
Design Rules ◽  
General Design ◽  
Mechanical Devices ◽  
Alternative Designs

Abstract There exists a need for methodologies on designing mechanical devices with flexible elements (compliant mechanisms). Many engineers currently have little direction in their designing efforts and have difficulty improving the performance of devices with flexible members. This paper presents a step towards a process and a set of rules for designing compliant mechanisms which aid engineers in selecting the best design concept among a set of alternatives. The approach is a more rational method for selecting and improving designs than the existing intuitive approach engineers now take. The general design rules aid the engineer in identifying good and bad design features and practices for devices containing flexible elements. The design rules help engineers avoid oversights and/or overlooked factors in design problems. Since many equivalent compliant mechanisms can be made from a single rigid-body solution, the rules can help engineers select between the compliant alternative designs.

Optimal Shear Key Interval for Offshore Shallow Foundations

2013 ◽  
Author(s):  
Xiaowei Feng ◽  
Susan Gourvenec
Keyword(s):  
Rigid Body ◽  
Shallow Foundations ◽  
Soil Plug ◽  
Shear Key ◽  
Optimal Capacity ◽  
Shear Keys ◽  
Optimal Spacing ◽  
Minimum Number ◽  
Rigid Body Displacement ◽  
Six Degree Of Freedom

Embedment of offshore shallow foundations is typically achieved by ‘skirts’, i.e. thin vertical plates that protrude from the underside of a foundation top plate and penetrate the seabed confining a soil plug. Skirted shallow foundations are often idealized as a solid, rigid element for geotechnical analysis of the foundation, on the assumption that sufficient skirts, or ‘shear keys’ will be provided to ensure that the deformable soil plug displaces as a rigid body. Should too few shear keys be provided, failure mechanisms involving deformation within the soil plug may occur, leading to a reduction in load-carrying capacity. There is currently no formal guidance regarding the optimal spacing of shear keys to ensure rigid body displacement of the soil plug. The absence of guidance may lead to unconservative designs if the number of shear keys is under estimated to save on fabrication or to conservative designs if additional shear keys are provided to minimize the risk associated with the uncertainty. Either case is undesirable and clear benefit is to be gained from a better understanding of shear key spacing. This paper presents guidance on the minimum number of shear keys required to achieve optimal capacity of square and rectangular skirted foundations (i.e. equivalent to that of a solid rigid foundation) under undrained generalized six degree-of-freedom loading in soft soils with linearly increasing shear strength with depth.

A New Method for Full Shaking Force Balancing of Planar Linkages by a Few Finite Positions

1996 ◽  
Author(s):  
Ting-Li Yang ◽  
Ming Zhang ◽  
Qiong Jin
Keyword(s):  
Basic Principle ◽  
Linear Equations ◽  
New Method ◽  
System Of Linear Equations ◽  
Position Data ◽  
Minimum Number ◽  
Spatial Linkages ◽  
Planar Linkages

Abstract A new method called “Finite Position Method” is presented in this paper. By means if this method, it is easy to obtain the condition for full shaking force balancing of planar linkages (FSFBPL), to derive the counter theorem and the minimum number of counterweights. The balancing condition could be generated easily via establishing and solving a system of linear equations using a few finite position data of the linkage. The basic principle of this method could be expanded to the study for balancing theory of the spatial linkages.

A General Theory for Complete Balancing of Shaking Force and Shaking Moment of Spatial Linkages Using Counterweights and Inertia-Counterweights

1994 ◽  
Author(s):  
Ting-Li Yang ◽  
Ming Zhang ◽  
Jian-Qin Zhang
Keyword(s):  
General Theory ◽  
Kinematic Equation ◽  
Force Moment ◽  
Minimum Number ◽  
Spatial Linkages ◽  
Independent Loops ◽  
Shaking Moment

Abstract The links of a spatial linkage with v independent loops can be divided into two parts — a set of v chord-links and a tree-system. Add a suitable counterweight to each chord-link for satisfying the certain conditions, under which, the v chord-links can be completely shaking force-moment-balanced by the counterweights and inertia-counterweights attached to the tree-system of the linkage; The conditions for complete balance of shaking force and shaking moment of the tree system can be written directly without extracting them from the kinematic equation of the linkage; A formula which define the minimum number of inertia-counterweights needed for a complete shaking-moment-balance and the criteria for selecting the optimum chord-link set have been presented. Two examples (a Bennett linkage and a spherical six-bar linkage) are provided.

scholarly journals The Coupler Surface of the RSRS Mechanism

2015 ◽  
Vol 8 (1) ◽  
Author(s):  
Nicolas Rojas ◽  
Aaron M. Dollar
Keyword(s):  
Rigid Body ◽  
Interested Reader ◽  
Implicit Equation ◽  
Spatial Mechanism ◽  
Full Equation ◽  
Sextic Curve ◽  
Spatial Linkages ◽  
Robotic Devices ◽  
Four Bar Linkage ◽  
Two Degree Of Freedom

Two degree-of-freedom (2-DOF) closed spatial linkages can be useful in the design of robotic devices for spatial rigid-body guidance or manipulation. One of the simplest linkages of this type, without any passive DOF on its links, is the revolute-spherical-revolute-spherical (RSRS) four-bar spatial linkage. Although the RSRS topology has been used in some robotics applications, the kinematics study of this basic linkage has unexpectedly received little attention in the literature over the years. Counteracting this historical tendency, this work presents the derivation of the general implicit equation of the surface generated by a point on the coupler link of the general RSRS spatial mechanism. Since the derived surface equation expresses the Cartesian coordinates of the coupler point as a function only of known geometric parameters of the linkage, the equation can be useful, for instance, in the process of synthesizing new devices. The steps for generating the coupler surface, which is computed from a distance-based parametrization of the mechanism and is algebraic of order twelve, are detailed and a web link where the interested reader can download the full equation for further study is provided. It is also shown how the celebrated sextic curve of the planar four-bar linkage is obtained from this RSRS dodecic.

Locating N Points of a Rigid Body on N Given Planes

2004 ◽  
Author(s):  
Charles W. Wampler
Keyword(s):  
Rigid Body ◽  
The Body ◽  
Forward Kinematics ◽  
Linear Least Squares ◽  
Geometric Problem ◽  
Quadratic Equations ◽  
Linear Least Squares Problem ◽  
Minimum Number ◽  
Parallel Link ◽  
And Robotics

This paper describes a method for finding the location of a rigid body such that N specified points of the body lie on N given planes in space. Of special interest is the case N = 6, which is the minimum number to fully constrain the body. This geometric problem arises in two seemingly disparate contexts: metrology, as a generalization of so-called “3-2-1” locating schemes; and robotics, as the forward kinematics problem for 6ES or 6SE parallel-link platform robots. For N = 6, the geometric problem can be formulated algebraically as 3 quadratic equations having, in general, eight possible solutions. We give a method for finding all eight solutions via an 8 × 8 eigenvalue problem. We also show that for N ≥ 7, the solution can be found uniquely as a linear least squares problem.

On the Number and Placement of Accelerometers for Angular Velocity and Acceleration Determination

2000 ◽  
Vol 123 (3) ◽  
pp. 552-554 ◽  
Author(s):  
Bruno Zappa ◽  
Giovanni Legnani ◽  
Anton J. van den Bogert ◽  
Riccardo Adamini
Keyword(s):  
Angular Velocity ◽  
Rigid Body ◽  
Sensor Placement ◽  
Body Acceleration ◽  
Minimum Number

This paper identifies the minimum number of accelerometers necessary to measure rigid body acceleration. Notwithstanding that only 9 scalar unknowns must be identified, 12 devices compose a minimum set of transducers. This redundancy is necessary to avoid singularities in the equations. Conditions for the sensor placement are given. It is also shown that when the determination of the angular velocity is not required, a reduced set of 9 sensors can be adopted.

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