Kinematic analysis and deformation of a planar lattice with an arbitrary number of panels

2020 ◽  
pp. 15-19
Author(s):  
M.N. Kirsanov
Keyword(s):  
Exact Solution ◽  
Kinematic Analysis ◽  
Arbitrary Number ◽  
Design Parameters ◽  
Lattice Deformation ◽  
Planar Lattice ◽  
Force Loading

Formulae are obtained for calculating the deformations of a statically determinate lattice under the action of two types of loads in its plane, depending on the number of panels located along one side of the lattice. Two options for fixing the lattice are analyzed. Cases of kinematic variability of the structure are found. The distribution of forces in the rods of the lattice is shown. The dependences of the force loading of some rods on the design parameters are obtained. Keywords: truss, lattice, deformation, exact solution, deflection, induction, Maple system. [email protected]

Analytical Calculation of Deformations and Kinematic Analysis of a Flat Truss with an Arbitrary Number of Panels

2021 ◽  
pp. 113-122
Author(s):  
М. Н. Кирсанов ◽  
О. В. Воробьев
Keyword(s):  
Kinematic Analysis ◽  
Arbitrary Number ◽  
Numerical Solutions ◽  
Optimization Problems ◽  
Analytical Calculation ◽  
Middle Part ◽  
Asymptotic Approximations ◽  
Induction Method ◽  
Particular Solutions

Постановка задачи. Разыскиваются аналитические зависимости прогиба и смещения опоры плоской фермы решетчатого вида от числа панелей. Ферма имеет сдвоенную решетку, прямолинейный нижний и приподнятый в средней части верхний пояс. Результаты. Для двух видов нагружения по формуле Максвелла-Мора получены аналитические зависимости прогибов конструкции от нагрузки, размеров и числа панелей. Для обобщения серии частных решений с различным числом панелей ферм на произвольный случай использован метод индукции и аналитические возможности системы компьютерной математики Maple. Для некоторых решений получены асимптотические приближения. Показано распределение усилий в элементах фермы. Выводы. Полученные формулы могут быть использованы в задачах оптимизации и как тестовые для оценки приближенных численных решений. Выявлены случаи геометрической изменяемости фермы при числе панелей, кратном трем. Приведен алгоритм выявления соответствующего распределения возможных скоростей шарниров. Statement of the problem. Analytical dependences of the deflection and displacement of the support of a flat lattice truss on the number of panels are being sought. The truss has a double lattice, a rectilinear lower belt and an upper belt raised in the middle part. Results. For two types of loading, according to the Maxwell-Mohr formula, analytical dependences of the deflections of the structure on the load, dimensions and number of panels are obtained. To generalize a series of particular solutions for trusses with different numbers of panels for an arbitrary case, the induction method and the analytical capabilities of the Maple computer mathematics system were used. For some solutions, asymptotic approximations are obtained. The distribution of forces in the rods of the structure is shown. Conclusions. The obtained formulas can be used in optimization problems and as test ones for evaluating approximate numerical solutions. Cases of geometric variability of the truss with the number of panels being a multiple of three are revealed. An algorithm for identifying the corresponding distribution of possible velocities of the joints is presented.

Analysis of mechanical errors in disc cam mechanisms

2005 ◽  
Vol 219 (2) ◽  
pp. 209-224 ◽  
Author(s):  
L-I Wu ◽  
W-T Chang
Keyword(s):  
Exact Solution ◽  
Analytical Method ◽  
Sudden Change ◽  
Design Parameters ◽  
Combined Effects ◽  
Worst Case ◽  
Cam Mechanism ◽  
Radial Dimension ◽  
Cam Profile ◽  
Shift Angle

This paper presents an analytical method for analysing the mechanical errors of disc cam mechanisms. With the aid of parametric expressions of the cam profile and by employing the concept of equivalent linkage, the error of the follower motion that is due to the variation in each design parameter can be determined analytically. The resulting error equations do not really involve the location of the curvature centre of the cam profile, and thus locating the curvature centre of the cam profile is not essential. The method is validated through analysing a cam mechanism that has an invariant equivalent linkage, and thus an exact solution is available. Compared with the exact solutions, the predicted results have at least four-figure accuracy. For the roller follower cases, the pressure angle has most effect on the resulting error. Owing to the counteraction of the shift angle, the resulting error due to the radial dimension error of the cam profile has relatively smaller variation. In the worst case, owing to the combined effects of various design parameters, the accuracy of the follower motion may degrade considerably. The acceleration error functions have a sudden change at the ends of the motion.

scholarly journals Kinematic Analysis Of Tricept Parallel Manipulator

2012 ◽  
Vol 12 (5) ◽  
Author(s):  
Mir Amin Hosseini ◽  
Hamid-Reza Mohammadi Daniali
Keyword(s):  
Kinematic Analysis ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Geometric Constraints ◽  
Design Parameters ◽  
Forward Kinematics ◽  
Jacobian Matrices ◽  
Moving Platforms ◽  
Workspace Optimization

Parallel manipulators consist of fixed and moving platforms connected to each other with some actuated links. They have some significant advantages over their serial counterparts. While, they suffer from relatively small workspaces, complex kinematics relations and highly singular points within their workspaces. In this paper, forward kinematics of Tricept parallel manipulator is solved analytically and its workspace optimization is performed. This parallel manipulator has a complex degree of freedom, therefore leads to dimensional in-homogeneous Jacobian matrices. Thus, we divide some entries of the Jacobian by units of length, thereby producing a new Jacobian that is dimensionally homogeneous. Moreover, its workspace is parameterized using some design parameters. Then, using GA method, the workspace is optimized subjects to some geometric constraints. Finally, dexterity of the design is evaluated. Keywords- Kinematic, Workspace, Singularity, TriceptABSTRAK - Manipulator selari terdiri daripada platform tetap dan bergerak yang bersambung antara satu sama lain dengan beberapa pautan bergerak. Manipulator selari mempunyai beberapa kebaikan tertentu dibandingkan dengan yang bersamaan dengannya. Walaupun ia mempunyai ruang kerja yang sempit, hubungan kinematik kompleks dan titik tunggal tinggi dalam linkungan ruang kerjanya. Dalam kajian ini, kinematik ke hadapan manipulator selari Tricept diselesaikan secara analisa dan pengoptimuman ruang kerja dijalankan. Manipulator selari ini mempunyai darjah kebebasan yang kompleks, yang menyebabkan ia mendorong kepada kehomogenan dimensi matriks Jacobian. Catatan Jacobian dibahagikan kepada unit panjang, dimana ia menghasilkan Jacobian baru yang homogen dimensinya. Tambahan, ruang kerjanya diparameterkan dengan menggunakan beberapa parameter reka bentuk. Kemudian, dengan kaedah GA, ruang kerja mengoptimakan subjek kepada beberapa kekangan geometrik. Akhirnya, kecakatan reka bentuk dinilaikan.Keywords- Kinematic, Workspace, Singularity, Tricept

scholarly journals Studying Kinematics and Capacity of Tools of Organic Fertilizer Loader

2018 ◽  
Vol 7 (4.38) ◽  
pp. 1109
Author(s):  
Evgeny Evgenievich Demin ◽  
Pavel Ivanovich Pavlov ◽  
Rustam Rafitovich Khakimzyanov ◽  
Victor Alekseevich Mukhio ◽  
Andrey Anatolyevich Protasov
Keyword(s):  
Physicochemical Properties ◽  
Kinematic Analysis ◽  
Organic Fertilizer ◽  
Theoretical Background ◽  
Organic Fertilizers ◽  
Design Parameters ◽  
Loading Capacity ◽  
Operation Conditions ◽  
Load Handling ◽  
Tool Diameter

This article discusses the issue of theoretical background of capacity of new load handling tools of continuous loaders for organic fertilizers on the basis of kinematic analysis of their motion. Loader efficiency is estimated by a set of performances the main of which is loading capacity. The loading capacity is determined by design and kinematic parameters of tools. Theoretical determination of capacity is an important scientific task, its solution would permit to substantiate loader parameters for predetermined operation conditions. Kinematic analysis of spiral, vane, shredding screw load handling tools is performed. Capacity of shredding tools is determined as a function of design and operation parameters as well as physicochemical properties of organic fertilizers. The obtained equations take into account motion pattern of tools, kinematic and design parameters as well as physicochemical properties of manure. The capacity depends quadratically on tool diameter. Dependence on other parameters is in fact directly proportional. The influence of tool angular velocity and its forward velocity is related with trigonometric functions of rotation angles during separation and gripping of organic fertilizers.  

scholarly journals COMMENTS ON 'REVERSE AUCTION: THE LOWEST UNIQUE POSITIVE INTEGER GAME'

2008 ◽  
Vol 08 (01) ◽  
pp. C1-C4 ◽  
Author(s):  
A. P. FLITNEY
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Nash Equilibrium ◽  
Positive Integer ◽  
Arbitrary Number ◽  
Reverse Auction ◽  
Expected Payoff ◽  
Utility Maximizer ◽  
Computational Capability ◽  
Rational Players

In Zeng et al. [Fluct. Noise Lett. 7 (2007) L439–L447] the analysis of the lowest unique positive integer game is simplified by some reasonable assumptions that make the problem tractable for arbitrary numbers of players. However, here we show that the solution obtained for rational players is not a Nash equilibrium and that a rational utility maximizer with full computational capability would arrive at a solution with a superior expected payoff. An exact solution is presented for the three- and four-player cases and an approximate solution for an arbitrary number of players.

Body waves in a “real Earth”. Part I

1973 ◽  
Vol 63 (1) ◽  
pp. 145-156 ◽  
Author(s):  
A. Cisternas ◽  
O. Betancourt ◽  
A. Leiva
Keyword(s):  
Exact Solution ◽  
Theoretical Analysis ◽  
Power Series ◽  
Arbitrary Number ◽  
Body Waves ◽  
Reflection And Transmission Coefficients ◽  
Earth Model ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
The Earth

abstract A theoretical analysis of body waves in a “real Earth” is presented. The earth model consists of an arbitrary number of spherical liquid and solid layers. The algebraic part of the analysis deals with the way to obtain generalized rays out of the exact solution. It is shown that the Rayleigh matrix, and not the Rayleigh determinant, should be used to expand the solution into a power series of modified reflection and transmission coefficients in order to obtain rays.

Multistage Geared Geneva Mechanism

1979 ◽  
Vol 101 (1) ◽  
pp. 41-46 ◽  
Author(s):  
A. T. Yang ◽  
L. M. Hsia
Keyword(s):  
Kinematic Analysis ◽  
Dwell Time ◽  
Rational Design ◽  
Design Parameters ◽  
Design Concepts ◽  
The Family ◽  
Gear Trains ◽  
N Stage ◽  
Phase Angles ◽  
Fine Tune

Design concepts for an n-stage geared Geneva mechanism, which is an assembly of n Geneva mechanisms connected by (n−1) gear trains, are proposed in this paper. The dwell time produced by the system is a function of (n−1) phase angles, the combined number of slots on all the wheels and the number of pins on all cranks in the system. The introduction of phase angles into the family of design parameters is highly significant: it gives the engineer an added dimension in the design of intermittent mechanisms and it gives him the flexibility to fine-tune their dwell time. For illustrative purposes, the derivation for the dwell time and the kinematic analysis of a two-stage geared Geneva mechanism are treated in detail. It is hoped that the results, which are presented in the form of charts and graphs, would be useful for the rational design of intermittent mechanisms.

scholarly journals Sensitivity Analysis of the Orthoglide, a 3-DOF Translational Parallel Kinematic Machine

2004 ◽  
Author(s):  
Ste´phane Caro ◽  
Philippe Wenger ◽  
Fouad Bennis ◽  
Damien Chablat
Keyword(s):  
Sensitivity Analysis ◽  
Kinematic Analysis ◽  
Design Parameters ◽  
Analysis Method ◽  
Parallel Kinematic Machine ◽  
Vector Method ◽  
End Effector ◽  
Singular Configurations ◽  
Parallel Kinematic ◽  
Position And Orientation

This paper presents a sensitivity analysis of the Orthoglide, a 3-DOF translational Parallel Kinematic Machine. Two complementary methods are used to analyze its sensitivity to its dimensional and angular variations. First, a linkage kinematic analysis method is used to have a rough idea of the influence of the dimensional variations on the location of the end-effector, and shows that the variations in design parameters of the same type from one leg to another one have the same influence on the end-effector. However, this method does not allow the designer to know the influence of the variations in the parallelograms. Thus, a differential vector method is used to study the influence of the dimensional and angular variations in the parts of the manipulator, and particularly the variations in the parallelograms, on the position and orientation of the end-effector. It turns out that the isotropic kinematic configuration of the manipulator is the least sensitive one to its geometrical variations, contrary to the closest configurations to its kinematic singular configurations, which are the most sensitive to geometrical variations.

Design and Kinematic Analysis of Parallel Robot for Ankle Rehabilitation

2013 ◽  
Vol 446-447 ◽  
pp. 1279-1284 ◽  
Author(s):  
Muhammad Nazrin Shah Bin Shahrol Aman ◽  
Shafriza Nisha Bin Basah
Keyword(s):  
Kinematic Analysis ◽  
Parallel Mechanism ◽  
Weight Ratio ◽  
Parallel Robot ◽  
Ankle Injury ◽  
Design Parameters ◽  
Concept Generation ◽  
Embodiment Design ◽  
Ankle Rehabilitation ◽  
Rehabilitation Exercises

Ankle injury is one of the most common injuries in sports or domestic related accidents. This injury can usually be treated via a number of rehabilitation exercises. However, currently rehabilitation of ankle injury directly depends of physiotherapy session administered by experts; which is tedious and expensive in nature. In this paper, we proposed a concept based on parallel mechanism to assist patients undergoing ankle rehabilitation procedures. This is due to a number of advantages of parallel mechanism as compared to serial mechanism higher payload-to-weight ratio, structure rigidity, accuracy and relatively simple solution. We reported our design process; including the concept generation and selection according to a number of relevant design parameters. After which, followed by embodiment design involving kinematic analysis of the proposed mechanism. The findings, in terms of conceptual design and kinematic analysis should be able to provide an insight for ankle rehabilitation based on suitable parallel mechanism.

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