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.

The Kinematics of Motion Through Finitely Separated Positions

1967 ◽  
Vol 34 (3) ◽  
pp. 591-598 ◽  
Author(s):  
Bernard Roth
Keyword(s):  
General Theory ◽  
Rigid Body ◽  
Numerical Evaluation ◽  
Companion Paper ◽  
Numerical Examples ◽  
Circle Plane ◽  
Spatial Linkages ◽  
Special Points

A rigid body is studied in a series of finitely separated positions, in order to determine those points which lie on a special locus (a sphere, circle, plane, line, or cylinder). Equations governing these special points are derived and their numerical evaluation is discussed. Several numerical examples are presented. In a companion paper [21], these results are applied to the synthesis of spatial linkages, and special motions (e.g., planer and spherical) are incorporated into the general theory presented herein.

Five Position Synthesis of Spatial CC Dyads

1994 ◽  
Author(s):  
Andrew P. Murray ◽  
J. Michael McCarthy
Keyword(s):  
Rigid Body ◽  
Kinematic Chain ◽  
New Technique ◽  
Screw Axis ◽  
Fixed Axis ◽  
A New Technique ◽  
Position Synthesis

Abstract This paper presents a new technique for determining the fixed axes of spatial CC dyads for rigid body guidance through five finitely separated positions. A CC dyad is a kinematic chain consisting of a floating link connected by a cylindric joint to a crank which in turn is connected to ground by a second cylindric joint. The lines that can be axes of the fixed joint are shown to be obtained from a “compatibility platform” constructed from selected relative screw axes associated with the five specified displacements. We show that the screw axis of the displacement of this platform is a fixed axis of a CC dyad compatible with the five positions. Roth’s original example is presented to verify the calculations. The specialization of this procedure to planar and spherical five position synthesis is also presented.

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.

Two-Dimensional Rigid-Body Collisions With Friction

1992 ◽  
Vol 59 (3) ◽  
pp. 635-642 ◽  
Author(s):  
Yu Wang ◽  
Matthew T. Mason
Keyword(s):  
Rigid Body ◽  
Graphical Method ◽  
Correct Identification ◽  
Two Dimensional ◽  
Contact Mode ◽  
New Class ◽  
Tangential Impact ◽  
Approach Velocity ◽  
Conservation Principles ◽  
Analytical Expressions

This paper presents an analysis of a two-dimensional rigid-body collision with dry friction. We use Routh’s graphical method to describe an impact process and to determine the frictional impulse. We classify the possible modes of impact, and derive analytical expressions for impulse, using both Poisson’s and Newton’s models of restitution. We also address a new class of impacts, tangential impact, with zero initial approach velocity. Some methods for rigid-body impact violate energy conservation principles, yielding solutions that increase system energy during an impact. To avoid such anomalies, we show that Poisson’s hypothesis should be used, rather than Newton’s law of restitution. In addition, correct identification of the contact mode of impact is essential.

Passive Control Analysis and Design of Twin-Tower Structure with Chassis

2020 ◽  
Vol 20 (06) ◽  
pp. 2040010
Author(s):  
Qiaoyun Wu ◽  
Hai Feng ◽  
Shiye Xiao ◽  
Hongping Zhu ◽  
Xixuan Bai
Keyword(s):  
Minimum Energy ◽  
Degree Of Freedom ◽  
Vibration Energy ◽  
Control Analysis ◽  
Numerical Examples ◽  
Analysis And Design ◽  
Mdof Systems ◽  
Tower Structure ◽  
Passive Dampers ◽  
Analytical Expressions

In this paper, a symmetrical twin-tower structure with chassis connected with passive dampers is coupled as 2-DOF (degree of freedom) model. Using the stationary white noise as seismic excitation, the frequency–response function and the vibration energy expression of the symmetrical twin-tower structure are established based on the simplified 2-DOF model. Furthermore, based on the principle of minimum energy, the analytical expressions of the optimization parameters of two kinds of passive dampers are deduced, and the effectiveness of the dampers with optimized coefficients on structural control is verified by numerical examples of 2-DOF and MDOF (multi-degree-of-freedom) systems, respectively. Finally, the control effects of the two kinds of dampers under different control strategies on the responses of displacement of the top, base shear, structural vibration energy, and maximum inter-story drift of the symmetrical twin-tower structure are discussed through three-dimensional finite element numerical examples. It is verified that the analytical expressions of optimum parameters of the two kinds of dampers proposed based on the 2-DOF model are also beneficial to reduce the responses of the MDOF systems and actual engineering.

Estimation of Location and Orientation From Range Measurements

2015 ◽  
Author(s):  
Sai Krishna Kanth Hari ◽  
Swaroop Darbha
Keyword(s):  
Linear Programming ◽  
Rigid Body ◽  
Center Of Mass ◽  
Body Motion ◽  
Second Step ◽  
True Distance ◽  
Numerical Examples ◽  
Range Measurements ◽  
Motion Constraints

Localization is an important required task for enabling vehicle autonomy. Localization entails the determination of the position of the center of mass and orientation of a vehicle from the available measurements. In this paper, we focus on localization by using the range measurements available to a vehicle from the communication of its multiple onboard receivers with roadside beacons. The model proposed for measurement is as follows: the true distance between a receiver and a beacon is at most equal to a predetermined function of the range measurement. The proposed procedure for localization is as follows: Based on the range measurements specific to a receiver from the beacons, a finite LP (linear programming) is proposed to estimate the location of the receiver. The estimate is essentially the Chebychev center of the set of possible locations of the receiver. In the second step, the location estimates of the vehicle are corrected using rigid body motion constraints and the orientation of the rigid body is thus determined. Two numerical examples provided at the end corroborate the procedures developed in this paper.

scholarly journals ON SARMANOV MIXED ERLANG RISKS IN INSURANCE APPLICATIONS

2014 ◽  
Vol 45 (1) ◽  
pp. 175-205 ◽  
Author(s):  
Enkelejd Hashorva ◽  
Gildas Ratovomirija
Keyword(s):  
North American ◽  
Stochastic Models ◽  
Capital Allocation ◽  
Economic Capital ◽  
Individual Risk ◽  
Dependence Structure ◽  
Simulation Studies ◽  
Numerical Examples ◽  
Dependence Measures ◽  
Analytical Expressions

AbstractIn this paper we consider an extension to the aggregation of the FGM mixed Erlang risks, proposed by Cossette et al. (2013 Insurance: Mathematics and Economics, 52, 560–572), in which we introduce the Sarmanov distribution to model the dependence structure. For our framework, we demonstrate that the aggregated risk belongs to the class of Erlang mixtures. Following results from S. C. K. Lee and X. S. Lin (2010 North American Actuarial Journal, 14(1) 107–130), G. E. Willmot and X. S. Lin (2011 Applied Stochastic Models in Business and Industry, 27(1) 8–22), analytical expressions of the contribution of each individual risk to the economic capital for the entire portfolio are derived under both the TVaR and the covariance capital allocation principle. By analysing the commonly used dependence measures, we also show that the dependence structure is wide and flexible. Numerical examples and simulation studies illustrate the tractability of our approach.

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.

An Analytical and Geometrical Study of the Dzhanibekov and Tennis Racket Phenomena

2016 ◽  
Author(s):  
Oscar Rios ◽  
Takeyuki Ono ◽  
Hidenori Murakami ◽  
Thomas J. Impelluso
Keyword(s):  
Rigid Body ◽  
Complete Solution ◽  
Satellite System ◽  
Moment Of Inertia ◽  
Moving Frame ◽  
Solar Panels ◽  
Tennis Racket ◽  
Principal Moments Of Inertia ◽  
Moving Frame Method ◽  
Analytical Expressions

We consider the torque-free rotation of a rigid body with three distinct moment of inertia values and angular velocity components. As can be seen in the Dzhanibekov and tennis racket phenomena, rotations about the largest and smallest principal moments of inertia create stable rotations. However, when rotating about the principal intermediate moment of inertia, an unstable rotation is produced that leads to the basis of this phenomena. In this publication, the above phenomena are examined and explained analytically and applied to a satellite system to observe the change in trajectory as the solar panels and reflectors are deployed. To begin the derivation, the Euler torque-free equations for a rotating rigid body are formulated using the moving frame method. The derived equations are then non-dimensionalized and a complete analytical solution, including an expression for the non-dimensional period, is presented. Second, we further look at the limiting axisymmetric cases and examine the effect as the intermediate moment of inertia is varied. Lastly, the analytical expressions are compared with the numerical simulation to validate the results. The complete solution is then summarized and shown to clearly prove that the conservation of angular momentum is indeed preserved in the phenomena.

The Analysis of Convergence of Shell Element with Rigid Body Displacements

2013 ◽  
Vol 284-287 ◽  
pp. 963-967
Author(s):  
Yong Dan ◽  
Qing Wang
Keyword(s):  
Rigid Body ◽  
Trial Function ◽  
Shell Element ◽  
Rigid Displacement ◽  
Numerical Examples

Rigid body displacements have different form existing in shell element trial function, and there is a different opinion about its influence. It is borne out by adding rigid body displacements in isoperimetric shell element and solving numerical examples with several methods, that rigid displacement is so important for the convergence of shell element that shouldn’t be neglected.

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