On the Existence of Special Cases of Input Speed Doubling Linkage Mechanisms

2003 ◽  
Author(s):  
J. Rastegar ◽  
J. Zhang ◽  
L. Hua
Keyword(s):  
Fundamental Frequency ◽  
Force Transmission ◽  
Periodic Motions ◽  
Output Link ◽  
Practical Applications ◽  
Special Cases ◽  
Mode Of Operation ◽  
Full Rotation ◽  
Rocking Motion ◽  
Special Case

A special class of planar and spatial linkage mechanisms is presented in which for a continuous full rotation or continuous rocking motion of the input link, the output link undergoes two continuous rocking motions. In a special case of such mechanisms, for periodic motions of the input link with a fundamental frequency ω, the output motion is periodic but with a fundamental frequency of 2ω. In this paper, the above class of linkage mechanisms are referred to as speed-doubling linkage mechanisms. Such mechanisms can be cascaded to provide further doubling of the fundamental frequency (rocking motion) of the output motion. They can also be cascaded with other appropriate linkage mechanisms to obtain crank-rocker or crank-crank type of mechanisms. The conditions for the existence of speed-doubling linkage mechanisms are provided and their mode of operation is described in detail. Such speed-doubling mechanisms have practical applications, particularly when higher output speeds are desired, since higher output motions can be achieved with lower input speeds. Such mechanisms also appear to generally have force transmission and dynamics advantages over regular mechanisms designed to achieve similar output speeds.

Special Cases of Input Speed Doubling Linkage Mechanisms and Their Dynamics Advantage

2004 ◽  
Author(s):  
J. Rastegar ◽  
J. Zhang
Keyword(s):  
Fundamental Frequency ◽  
Linkage Mechanism ◽  
Practical Applications ◽  
Special Cases ◽  
Lower Amplitude ◽  
Full Rotation ◽  
Rocking Motion ◽  
Frequency Components ◽  
Special Case ◽  
Input Torque

In a recent study, Rastegar, et al. (2003), presented a special class of planar and spatial linkage mechanisms in which for a continuous full rotation or continuous rocking motion of the input link, the output link undergoes two continuous rocking motions. In a special case of such mechanisms, for periodic motions of the input link, the output motion is periodic with a doubled fundamental frequency. The above class of linkage mechanisms were referred to as “speed-doubling” linkage mechanisms. Such mechanisms can be cascaded to further double the fundamental frequency (rocking motion) of the output motion. They can also be cascaded with other linkage mechanisms to obtain crank-rocker or crank-crank type of mechanisms. The conditions for the existence of “speed-doubling” linkage mechanisms were also provided. In this paper, a study of the dynamics of a “speed-doubling” linkage mechanism is presented. It is shown that such mechanisms have dynamic advantage over regular mechanisms designed to achieve similar output motions. The main advantage of such mechanisms is shown to be their lower peak input torque requirement, and that the required torque generally has lower amplitude high-frequency components. The speed-doubling mechanisms have practical applications, particularly when higher output speeds are desired, since higher output motions can be achieved with lower input speeds and smaller motors.

Reduction of Induced Vibration Using Motion-Doubling Linkage Mechanisms

2006 ◽  
Author(s):  
J. Rastegar ◽  
J. Zhang
Keyword(s):  
High Speed ◽  
High Harmonic ◽  
Full Rotation ◽  
Rocking Motion ◽  
Points Of View ◽  
Harmonic Components ◽  
Input Motion ◽  
And Control ◽  
Special Case ◽  
Input Torque

In recent studies, the authors presented a special class of planar and spatial linkage mechanisms in which for a continuous full rotation or continuous rocking motion of the input link, the output link undergoes two continuous rocking motions. Such linkage mechanisms were referred to as the “motion-doubling” linkage mechanisms. It was also shown that in a special case of such mechanisms, the fundamental frequency of the input motion is doubled. This class of mechanisms generally has dynamics advantage over regular mechanisms designed to achieve similar gross output motions. In the present study, it is shown that in general and for the same gross output motion, motion-doubling mechanisms require lower input torques, and that the high harmonics of the input torque have smaller amplitudes. The high harmonic components present in the input torque are the main source of vibration and control problems in the system or device that the mechanism operates and its own structure. It is therefore concluded that when vibration and motion precision is of concern, such as in high-speed and precision machinery, motion-doubling mechanisms are generally more suitable from the potential vibration excitation and control points of view and actuating torque requirements.

Analytical Techniques for the Optimisation of Rocket Trajectories

1963 ◽  
Vol 14 (2) ◽  
pp. 105-124 ◽  
Author(s):  
Derek F. Lawden
Keyword(s):  
Gravitational Field ◽  
Artificial Satellite ◽  
Analytical Techniques ◽  
Present Position ◽  
Mayer Problem ◽  
Special Cases ◽  
Minimum Expenditure ◽  
Law Of Attraction ◽  
Special Case

SummaryThe development during the last two decades of analytical techniques for the solution of problems relating to the optimisation of rocket trajectories is outlined and the present position in this field of research is summarised. It is shown that the determination of optimal trajectories in a general gravitational field can be expressed as a Mayer problem from the calculus of variations. The known solution to such a problem is stated and applied, first to the special case of the launching of an artificial satellite into a circular orbit with minimum expenditure of propellant and, secondly, to the general astronautical problem of the economical transfer of a rocket between two terminals in a gravitational field. The special cases when the field is uniform and when it obeys an inverse square law of attraction to a point are then considered, and the paper concludes with some remarks concerning areas in which further investigations are necessary.

scholarly journals Water entry of an expanding wedge/plate with flow detachment

2016 ◽  
Vol 797 ◽  
pp. 322-344 ◽  
Author(s):  
Yuriy A. Semenov ◽  
Guo Xiong Wu
Keyword(s):  
Free Surface ◽  
General Solution ◽  
Water Entry ◽  
Hodograph Method ◽  
Fixed Length ◽  
Pressure Distributions ◽  
Initial Stage ◽  
Special Cases ◽  
Wedge Plate ◽  
Special Case

A general similarity solution for water-entry problems of a wedge with its inner angle fixed and its sides in expansion is obtained with flow detachment, in which the speed of expansion is a free parameter. The known solutions for a wedge of a fixed length at the initial stage of water entry without flow detachment and at the final stage corresponding to Helmholtz flow are obtained as two special cases, at some finite and zero expansion speeds, respectively. An expanding horizontal plate impacting a flat free surface is considered as the special case of the general solution for a wedge inner angle equal to ${\rm\pi}$. An initial impulse solution for a plate of a fixed length is obtained as the special case of the present formulation. The general solution is obtained in the form of integral equations using the integral hodograph method. The results are presented in terms of free-surface shapes, streamlines and pressure distributions.

Optimal Design of a 2-UPR-RPU Parallel Manipulator

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
Feibo Wang ◽  
Qiaohong Chen ◽  
Qinchuan Li
Keyword(s):  
Optimal Design ◽  
Parallel Manipulator ◽  
Design Space ◽  
Parameter Design ◽  
Optimal Parameters ◽  
Force Transmission ◽  
Universal Joint ◽  
Practical Applications ◽  
Optimum Region ◽  
Dimensional Optimization

This paper investigates dimensional optimization of a 2-UPR-RPU parallel manipulator (where U is a universal joint, P a prismatic pair, and R a revolute pair). First, the kinematics and screws of the mechanism are analyzed. Then, three indices developed from motion/force transmission are proposed to evaluate the performance of the 2-UPR-RPU parallel manipulator. Based on the performance atlases obtained, a set of optimal parameters are selected from the optimum region within the parameter design space. Finally, the optimized parameters are determined for practical applications.

scholarly journals On Reay's Relaxed Tverberg Conjecture and Generalizations of Conway's Thrackle Conjecture

10.37236/6516 ◽  
2018 ◽  
Vol 25 (3) ◽  
Author(s):  
Megumi Asada ◽  
Ryan Chen ◽  
Florian Frick ◽  
Frederick Huang ◽  
Maxwell Polevy ◽  
...  
Keyword(s):  
Geometric Property ◽  
Convex Sets ◽  
Convex Hulls ◽  
Open Problems ◽  
Higher Dimensional ◽  
Special Cases ◽  
Minimum Number ◽  
Point Set ◽  
Colored Version ◽  
Special Case

Reay's relaxed Tverberg conjecture and Conway's thrackle conjecture are open problems about the geometry of pairwise intersections. Reay asked for the minimum number of points in Euclidean $d$-space that guarantees any such point set admits a partition into $r$ parts, any $k$ of whose convex hulls intersect. Here we give new and improved lower bounds for this number, which Reay conjectured to be independent of $k$. We prove a colored version of Reay's conjecture for $k$ sufficiently large, but nevertheless $k$ independent of dimension $d$. Pairwise intersecting convex hulls have severely restricted combinatorics. This is a higher-dimensional analogue of Conway's thrackle conjecture or its linear special case. We thus study convex-geometric and higher-dimensional analogues of the thrackle conjecture alongside Reay's problem and conjecture (and prove in two special cases) that the number of convex sets in the plane is bounded by the total number of vertices they involve whenever there exists a transversal set for their pairwise intersections. We thus isolate a geometric property that leads to bounds as in the thrackle conjecture. We also establish tight bounds for the number of facets of higher-dimensional analogues of linear thrackles and conjecture their continuous generalizations.

Zero Knowledge Proofs

2018 ◽  
pp. 111-123 ◽  
Author(s):  
Kannan Balasubramanian ◽  
Mala K.
Keyword(s):  
Real World ◽  
The Other ◽  
Interactive Proof ◽  
Zero Knowledge ◽  
Practical Applications ◽  
Proof Of Knowledge ◽  
Real World Applications ◽  
Special Case ◽  
Zero Knowledge Proof

Zero knowledge protocols provide a way of proving that a statement is true without revealing anything other than the correctness of the claim. Zero knowledge protocols have practical applications in cryptography and are used in many applications. While some applications only exist on a specification level, a direction of research has produced real-world applications. Zero knowledge protocols, also referred to as zero knowledge proofs, are a type of protocol in which one party, called the prover, tries to convince the other party, called the verifier, that a given statement is true. Sometimes the statement is that the prover possesses a particular piece of information. This is a special case of zero knowledge protocol called a zero-knowledge proof of knowledge. Formally, a zero-knowledge proof is a type of interactive proof.

scholarly journals Budget Feasible Mechanisms on Matroids

Algorithmica ◽  
2020 ◽  
Author(s):  
Stefano Leonardi ◽  
Gianpiero Monaco ◽  
Piotr Sankowski ◽  
Qiang Zhang
Keyword(s):  
Polynomial Time ◽  
Private Information ◽  
Independent Set ◽  
Deterministic Algorithm ◽  
Matroid Intersection ◽  
Practical Applications ◽  
Incentive Compatible ◽  
The Cost ◽  
Special Case ◽  
Budget Feasible

AbstractMotivated by many practical applications, in this paper we study budget feasible mechanisms with the goal of procuring an independent set of a matroid. More specifically, we are given a matroid $${\mathcal {M}}=(E,{\mathcal {I}})$$ M = ( E , I ) . Each element of the ground set E is controlled by a selfish agent and the cost of the element is private information of the agent itself. A budget limited buyer has additive valuations over the elements of E. The goal is to design an incentive compatible budget feasible mechanism which procures an independent set of the matroid of largest possible value. We also consider the more general case of the pair $${\mathcal {M}}=(E,{\mathcal {I}})$$ M = ( E , I ) satisfying only the hereditary property. This includes matroids as well as matroid intersection. We show that, given a polynomial time deterministic algorithm that returns an $$\alpha $$ α -approximation to the problem of finding a maximum-value independent set in $${\mathcal {M}}$$ M , there exists an individually rational, truthful and budget feasible mechanism which is $$(3\alpha +1)$$ ( 3 α + 1 ) -approximated and runs in polynomial time, thus yielding also a 4-approximation for the special case of matroids.

scholarly journals Minimizing Total Completion Time For Preemptive Scheduling With Release Dates And Deadline Constraints

2014 ◽  
Vol 39 (1) ◽  
pp. 17-26 ◽  
Author(s):  
Cheng He ◽  
Hao Lin ◽  
Yixun Lin ◽  
Junmei Dou
Keyword(s):  
Completion Time ◽  
Total Completion Time ◽  
Release Dates ◽  
Preemptive Scheduling ◽  
Release Date ◽  
Enumeration Algorithm ◽  
Processing Times ◽  
Special Cases ◽  
Deadline Constraints ◽  
Special Case

Abstract It is known that the single machine preemptive scheduling problem of minimizing total completion time with release date and deadline constraints is NP- hard. Du and Leung solved some special cases by the generalized Baker's algorithm and the generalized Smith's algorithm in O(n2) time. In this paper we give an O(n2) algorithm for the special case where the processing times and deadlines are agreeable. Moreover, for the case where the processing times and deadlines are disagreeable, we present two properties which could enable us to reduce the range of the enumeration algorithm

A New Incremental Harmonic Balance Method With Two Time Scales for Quasi-Periodic Motions of an Axially Moving Beam With Internal Resonance Under Single-Tone External Excitation

2019 ◽  
Author(s):  
Jianliang Huang ◽  
Weidong Zhu
Keyword(s):  
Fundamental Frequency ◽  
Time Scales ◽  
Harmonic Balance ◽  
Axially Moving Beam ◽  
Periodic Motions ◽  
Moving Beam ◽  
Frequency Components ◽  
Incremental Harmonic Balance ◽  
Axially Moving ◽  
Ihb Method

Abstract In this work, a new incremental harmonic balance (IHB) method with two time scales, where one is a fundamental frequency, and the other is an interval distance of two adjacent frequencies, is proposed for quasi-periodic motions of an axially moving beam with three-to-one internal resonance under singletone external excitation. It is found that the interval frequency of every two adjacent frequencies, located around the fundamental frequency or one of its integer multiples, is fixed due to nonlinear coupling among resonant vibration modes. Consequently, only two time scales are used in the IHB method to obtain all incommensurable frequencies of quasi-periodic motions of the axially moving beam. The present IHB method can accurately trace from periodic responses of the beam to its quasi-periodic motions. For periodic responses of the axially moving beam, the single fundamental frequency is used in the IHB method to obtain solutions. For quasi-periodic motions of the beam, the present IHB method with two time scales is used, along with an amplitude increment approach that includes a large number of harmonics, to determine all the frequency components. All the frequency components and their corresponding amplitudes, obtained from the present IHB method, are in excellent agreement with those from numerical integration using the fourth-order Runge-Kutta method.

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