Momentum Balancing of Four-Bar Linkages

1976 ◽  
Vol 98 (4) ◽  
pp. 1289-1295 ◽  
Author(s):  
J. L. Wiederrich ◽  
B. Roth
Keyword(s):  
Angular Momentum ◽  
Center Of Mass ◽  
Primary Objective ◽  
Simple Design ◽  
Numerical Examples ◽  
Mass Distributions ◽  
Computer Based ◽  
Four Bar Linkage ◽  
Shaking Moment

The primary objective in this work is the determination of conditions for reducing the angular momentum fluctuations (i.e., vibration) transmitted to the frame of a completely force balanced four-bar linkage. This approach leads to relatively simple design equations for determining the inertial properties of the links for good momentum balancing. The essence of this procedure is that it yields analytical results as opposed to the computer-based search techniques required by most previously published methods, which are based on reducing the shaking forces and moments rather than the momentum fluctuations. Furthermore, this method allows for off-line mass distributions (i.e., the center of mass of the link is not on the line of pivots) and, as we show in the paper, this can result in better momentum balancing than the in-line case to which most previous works have been restricted. Some numerical examples are given and the results are compared to similar results obtained by minimizing the RMS shaking moment.

Complete Balancing of Multicylinder Engines Without Requiring Harmonic Balancers

1995 ◽  
Author(s):  
Cemil Bagci
Keyword(s):  
Angular Momentum ◽  
Center Of Mass ◽  
New Method ◽  
Harmonic Force ◽  
Vector Method ◽  
Numerical Examples ◽  
Single Cylinder ◽  
Linearly Independent ◽  
Phase Angles ◽  
Shaking Moment

Abstract Presently used balancing methods for multicylinder engines and pumps are for partial balancing. As a result the complete shaking force, shaking torque, and shaking moment balancings of engines require the use of harmonic force and harmonic torque and moment balancers. This article presents a new method for complete shaking force and shaking moment balancing of multicylinder engines that requires no harmonic balancers. This is achieved by keeping the total center of mass of each slider crank loop stationary, where the design equations are developed using a linearly independent mass vector method. Balancing the shaking force also balances the shaking moment. Shaking torque is balanced by eliminating the angular momentum of each mechanism loop and by arranging the phase angles of the crank throws. Four-, six-, and eight-cylinder engines are balanced in the numerical examples given. Two methods of completely balancing single-cylinder engines are also given.

Complete Shaking Force and Shaking Moment Balancing of Link Mechanisms Using Balancing Idler Loops

1982 ◽  
Vol 104 (2) ◽  
pp. 482-493 ◽  
Author(s):  
Cemil Bagci
Keyword(s):  
Angular Momentum ◽  
Total Angular Momentum ◽  
Center Of Mass ◽  
Numerical Example ◽  
Shaking Moment

A method for completely balancing the shaking forces and shaking moments in mechanisms is presented. The method introduces shaking moment balancing idler parallelogram loop (or loops) which transfers the motion of a coupler link to a shaft on the frame of the mechanism, where the rotary balancers balance the shaking moment. The complete balancing of a mechanism is accomplished by maintaining the total center of mass of the mechanism stationary meanwhile achieving that the total angular momentum of the moving links of the mechanism vanishes. Positioning of the idler loops is illustrated for a series of multiloop mechanisms. Theorems on the complete balancing of shaking forces and shaking moments in mechanisms are established. Design equations for completely balancing some single and multiloop mechanisms are given. A numerical example is included.

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 Infrared effects in the late stages of black hole evaporation

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Éanna É. Flanagan
Keyword(s):  
Black Hole ◽  
Angular Momentum ◽  
Center Of Mass ◽  
Planck Scale ◽  
Black Hole Mass ◽  
Order Unity ◽  
Intrinsic Angular Momentum ◽  
Hole Position ◽  
Late Stages ◽  
Shear Tensor

Abstract As a black hole evaporates, each outgoing Hawking quantum carries away some of the black holes asymptotic charges associated with the extended Bondi-Metzner-Sachs group. These include the Poincaré charges of energy, linear momentum, intrinsic angular momentum, and orbital angular momentum or center-of-mass charge, as well as extensions of these quantities associated with supertranslations and super-Lorentz transformations, namely supermomentum, superspin and super center-of-mass charges (also known as soft hair). Since each emitted quantum has fluctuations that are of order unity, fluctuations in the black hole’s charges grow over the course of the evaporation. We estimate the scale of these fluctuations using a simple model. The results are, in Planck units: (i) The black hole position has a uncertainty of $$ \sim {M}_i^2 $$ ∼ M i 2 at late times, where Mi is the initial mass (previously found by Page). (ii) The black hole mass M has an uncertainty of order the mass M itself at the epoch when M ∼ $$ {M}_i^{2/3} $$ M i 2 / 3 , well before the Planck scale is reached. Correspondingly, the time at which the evaporation ends has an uncertainty of order $$ \sim {M}_i^2 $$ ∼ M i 2 . (iii) The supermomentum and superspin charges are not independent but are determined from the Poincaré charges and the super center-of-mass charges. (iv) The supertranslation that characterizes the super center-of-mass charges has fluctuations at multipole orders l of order unity that are of order unity in Planck units. At large l, there is a power law spectrum of fluctuations that extends up to l ∼ $$ {M}_i^2/M $$ M i 2 / M , beyond which the fluctuations fall off exponentially, with corresponding total rms shear tensor fluctuations ∼ MiM−3/2.

scholarly journals Measuring the quartic Higgs self-coupling at a multi-TeV muon collider

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
M. Chiesa ◽  
F. Maltoni ◽  
L. Mantani ◽  
B. Mele ◽  
F. Piccinini ◽  
...  
Keyword(s):  
Higgs Boson ◽  
Center Of Mass ◽  
Mass Energy ◽  
Simple Analysis ◽  
Proton Proton ◽  
Coupling Interaction ◽  
Center Of Mass Energy ◽  
Muon Collider ◽  
Better Than

Abstract Measuring the shape of the Higgs boson potential is of paramount importance, and will be a challenging task at current as well as future colliders. While the expectations for the measurement of the trilinear Higgs self-coupling are rather promising, an accurate measurement of the quartic self-coupling interaction is presently considered extremely challenging even at a future 100 TeV proton-proton collider. In this work we explore the sensitivity that a muon collider with a center of mass energy in the multi-TeV range and luminosities of the order of 1035cm−2s−1, as presently under discussion, might provide, thanks to a rather large three Higgs-boson production and to a limited background. By performing a first and simple analysis, we find a clear indication that a muon collider could provide a determination of the quartic Higgs self-coupling that is significantly better than what is currently considered attainable at other future colliders.

scholarly journals Evaluation of hydrological and cryospheric angular momentum estimates based on GRACE, GRACE-FO and SLR data for their contributions to polar motion excitation

2021 ◽  
Vol 73 (1) ◽  
Author(s):  
Justyna Śliwińska ◽  
Jolanta Nastula ◽  
Małgorzata Wińska
Keyword(s):  
Angular Momentum ◽  
Spherical Harmonic ◽  
Polar Motion ◽  
Spectral Band ◽  
Water Storage ◽  
Terrestrial Water Storage ◽  
Terrestrial Water ◽  
High Consistency ◽  
Polar Motion Excitation

AbstractIn geodesy, a key application of data from the Gravity Recovery and Climate Experiment (GRACE), GRACE Follow-On (GRACE-FO), and Satellite Laser Ranging (SLR) is an interpretation of changes in polar motion excitation due to variations in the Earth’s surficial fluids, especially in the continental water, snow, and ice. Such impacts are usually examined by computing hydrological and cryospheric polar motion excitation (hydrological and cryospheric angular momentum, HAM/CAM). Three types of GRACE and GRACE-FO data can be used to determine HAM/CAM, namely degree-2 order-1 spherical harmonic coefficients of geopotential, gridded terrestrial water storage anomalies computed from spherical harmonic coefficients, and terrestrial water storage anomalies obtained from mascon solutions. This study compares HAM/CAM computed from these three kinds of gravimetric data. A comparison of GRACE-based excitation series with HAM/CAM obtained from SLR is also provided. A validation of different HAM/CAM estimates is conducted here using the so-called geodetic residual time series (GAO), which describes the hydrological and cryospheric signal in the observed polar motion excitation. Our analysis of GRACE mission data indicates that the use of mascon solutions provides higher consistency between HAM/CAM and GAO than the use of other datasets, especially in the seasonal spectral band. These conclusions are confirmed by the results obtained for data from first 2 years of GRACE-FO. Overall, after 2 years from the start of GRACE-FO, the high consistency between HAM/CAM and GAO that was achieved during the best GRACE period has not yet been repeated. However, it should be remembered that with the systematic appearance of subsequent GRACE-FO observations, this quality can be expected to increase. SLR data can be used for determination of HAM/CAM to fill the one-year-long data gap between the end of GRACE and the start of the GRACE-FO mission. In addition, SLR series could be particularly useful in determination of HAM/CAM in the non-seasonal spectral band. Despite its low seasonal amplitudes, SLR-based HAM/CAM provides high phase consistency with GAO for annual and semiannual oscillation.

scholarly journals Study on Optimal Placement and Reasonable Number of Viscoelastic Dampers by Improved Weight Coefficient Method

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Ji-ting Qu ◽  
Hong-nan Li
Keyword(s):  
Mathematical Model ◽  
Weight Coefficient ◽  
Optimal Placement ◽  
Optimal Method ◽  
Analogy Method ◽  
Numerical Examples ◽  
Viscoelastic Dampers ◽  
Reasonable Number ◽  
Coefficient Method

A new optimal method is presented by combining the weight coefficient with the theory of force analogy method. Firstly, a new mathematical model of location index is proposed, which deals with the determination of a reasonable number of dampers according to values of the location index. Secondly, the optimal locations of dampers are given. It can be specific from stories to spans. Numerical examples are illustrated to verify the effectiveness and feasibility of the proposed mathematical model and optimal method. At last, several significant conclusions are given based on numerical results.

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