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Design Alternatives of Network of Altmann Linkages
Abstract and Figures
This paper presents a method of building deployable network assemblies derived from the single degree
of freedom (DoF) over constrained Altmann linkage as a basic module. The method is based on assembling
linkages with common links and joints or overlapping with extra R or 2R joints. New loops are
emerged with overlapping method. The networks created have a single DoF, are over-constrained and
have both fully deployed and folded configurations. The computer-aided models (CAD) are used to
demonstrate these derived novel mechanisms
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... Останнім часом опубліковано багато робіт із дослідження й проектування схем і конструкцій захоплювачів різного призначення, у тому числі й механічних стрижньових. Широко висвіт-лені результати розробок нових кінематичних схем захоплювачів, методики й результати кінематичних і кінетостатичних розрахунків, проблеми компонування й конструювання вузлів і деталей захоплювальних пристроїв[1, 3,8,9,11,17,18]. Проте залишаються поза увагою питання метричного синтезу схеми механізму, хоча визначення його оптимальних розмірів і положень ланок, встановлення залежностей між швидкостями й пришвидшеннями точок є початковою й важливою задачею проектувальника [5,10]. ...
... Рис. 5. Перетин об'ємної фігури залежності UV (φ, σ, γ) дезаксіального кривошипно-повзункового механізму площиною критерію оптимізації (γ = 0,8) (а), графіки UV у робочому діапазоні φ експлуатації захоплювача з симетричним відхиленням від критерію оптимізації для деяких відносних параметрів механізму (1-σ = 2 і γ=0,7; 2-σ = 1,1 і γ=0,82; 3-σ = 0,908 і γ=0,902; 4-σ = 0,524 і γ=0,902) (б), кути тиску:в обертальній парі шатун -кривошип (4,5,6), у поступальній парі напрямна -повзун (7,8,9) (в), графіки UV й кутів тиску для механізму з параметром σ =1,1і γ=0,82 й визначення для нього кута експлуатації (1-UV, 2-θ12, 3-θ23) (г) Fig. 5. Cross section of the volume figure of the UV (φ, σ, γ) dependence of the de-axial crank-slider mechanism by the plane of the optimization criterion (γ = 0.8) (a), the UV graphs in the operating range φ of the gripping device operation with a symmetric deviation from the optimization criterion for some relative parameters of the mechanism (1 -σ = 2 and γ = 0.7; 2 -σ = 1.1 and γ = 0.82; 3 -σ = 0.908 and γ = 0.902; 4 -σ = 0.524 and γ = 0.902) (b), angles of pressure: in the rotating pair connecting rodcrank (4,5,6), in thesliding pair a guidea slider (7,8,9) (c), graphs of UV and pressure angles for the mechanism with the parameter σ = 1.1 and γ = 0.82 and the definition of operation angle for it (1 -UV, 2 -θ12, 3 -θ23)(d) Кут тиску в поступальній парі визначимо за залежністю: ...
... Рис. 5. Перетин об'ємної фігури залежності UV (φ, σ, γ) дезаксіального кривошипно-повзункового механізму площиною критерію оптимізації (γ = 0,8) (а), графіки UV у робочому діапазоні φ експлуатації захоплювача з симетричним відхиленням від критерію оптимізації для деяких відносних параметрів механізму (1-σ = 2 і γ=0,7; 2-σ = 1,1 і γ=0,82; 3-σ = 0,908 і γ=0,902; 4-σ = 0,524 і γ=0,902) (б), кути тиску:в обертальній парі шатун -кривошип (4,5,6), у поступальній парі напрямна -повзун (7,8,9) (в), графіки UV й кутів тиску для механізму з параметром σ =1,1і γ=0,82 й визначення для нього кута експлуатації (1-UV, 2-θ12, 3-θ23) (г) Fig. 5. Cross section of the volume figure of the UV (φ, σ, γ) dependence of the de-axial crank-slider mechanism by the plane of the optimization criterion (γ = 0.8) (a), the UV graphs in the operating range φ of the gripping device operation with a symmetric deviation from the optimization criterion for some relative parameters of the mechanism (1 -σ = 2 and γ = 0.7; 2 -σ = 1.1 and γ = 0.82; 3 -σ = 0.908 and γ = 0.902; 4 -σ = 0.524 and γ = 0.902) (b), angles of pressure: in the rotating pair connecting rodcrank (4,5,6), in thesliding pair a guidea slider (7,8,9) (c), graphs of UV and pressure angles for the mechanism with the parameter σ = 1.1 and γ = 0.82 and the definition of operation angle for it (1 -UV, 2 -θ12, 3 -θ23)(d) Кут тиску в поступальній парі визначимо за залежністю: ...
Мета. Основна мета роботи – виконати кінематичний синтез схем кривошипно-повзункового захоплювального пристрою за критерієм сталості потужності приводу механізму з обмеженнями щодо припустимих кутів тиску в кінематичних парах. Методика. Досягнення поставленої мети здійснюється засобами теорії механізмів і машин за допомогою аналітичного методу трикутників Озолса кінематики пласких стрижньових механізмів та математичним моделюванням руху ланок. Результати. Десятиланковий стрижневий механізм захоплювача побудований на основі спареного паралелограмного кривошипно-повзункового механізму з ведучим повзуном. Для захоплювача, побудованого на основі стрижньової схеми, доцільно оптимальне проектування з використанням критеріїв передавання руху, або індексів передачі. Для забезпечення постійного зусилля затискання для об’єктів різної товщини бажано, щоб потужність приводу була сталою, а енергетичні витрати мінімальними. За критерій оптимізації взято відношення швидкості ведучої ланки механізму до проекції вектора швидкості точки веденої ланки на напрям вектора сили затискання (енергетичний трансмісійний індекс). Найменші енергетичні витрати мають місце, коли індекс близький до одиниці. Отримані аналітичні залежності для визначення швидкісних функцій центрального й дезаксіального кривошипно-повзункового механізму захоплювача, які зручні для аналізу й моделювання. На їх основі виконаний енергетичний синтез геометричних параметрів механізму захоплювального пристрою за критерієм найменшого відхилення від одиниці енергетичного трансмісійного індексу. З’ясовано, що практичне використання захоплювача на основі центрального кривошипно-повзункового механізму за даним критерієм украй обмежене. Розширює можливості захоплювача використання в його схемі дезаксіального кривошипно-повзункового механізму, а найкращі результати можуть бути отримані в схемі, де дезаксіал менший за кривошип. Визначені конкретні значення відносних параметрів довжин ланок і діапазони повороту кривошипа центрального й дезаксіального кривошипно-повзункового механізму захоплювача, що найкраще відповідають критерію оптимізації й задовольняють обмеженням за кутами тиску. Наукова новизна. Уперше введений новий критерій передавання руху – енергетичний трансмісійний індекс. За цим критерієм проведений кінематичний синтез захоплювального пристрою, побудованого на основі спареного кривошипно-повзункового механізму. Практична значимість. Запропоновані практичні рекомендації щодо відносних розмірів і розташування ланок механізму для центрального й дезаксіального кривошипно-повзункового механізму захоплювача, які реалізують вимоги критерію оптимізації та обмеження щодо припустимих кутів тиску.
... Besides, a family of one-DOF mobile assemblies of Myard linkages has been created according to tiling ways with different twist angles [21,22]. In addition, Altmann linkages with overlapping method [23], threefold-symmetric Bricard linkage by forming scissor connectors [24] or replacing hinges with one-DOF mechanisms [25], thick-panel origami patterns [26,27] can construct single-DOF deployable structures. For the 3D tessellations of linkages, deployable mast based on Hoekens linkages [28], Hoberman ball based on Sarrus and scissor-like linkages [29], foldable octahedron [30], kirigami-inspired foldable truncated octahedron [31] and other foldable polyhedrons [32][33][34][35][36][37][38][39][40] are constructed with excellent symmetric properties. ...
Multiple mobile assemblies have been created based on two-dimensional tessellations of linkages for deployable structures. However, few three-dimensional tessellations of linkages have been created, especially mobile assemblies with bifurcation. Here, we proposed four types of mobile assemblies of kaleidocycles, a special type of threefold-symmetric Bricard linkages, based on cubic cellulation and symmetry. Kinematic analysis of them is carried out based on the matrix method and numerical method. Two assemblies have bifurcations with two motion paths following cuboid symmetry and tetrahedral symmetry, respectively. Meanwhile, the other two have one motion path with single degree of freedom. The designing process facilitates the creation of new mobile assemblies under symmetry and the four assemblies have the potential application for designing metamaterials.
... Chen [13] improved it with alternative parameters by avoiding bifurcation singularity. Altmann 6R linkages [14] can also be expanded into a square. Lyu [15] used type III Bricard linkages to fold square and rhombus into a bundle. ...
In this paper, a series of deployable polygon mechanisms (DGMs) and deployable polyhedron mechanisms (DPMs) are proposed. Firstly, we propose a new plane-symmetric 7R unit with folded lateral edges. Kinematics and suitable parameter values are calculated to realize full expansion. N-pyramid and N-frustum and a larger DPM are designed. Secondly, we propose a new RRR chain to connect existing deployable units. Threefold Bricard mechanism and alternative Bennett mechanism are used as two examples to fold triangular and square frustum into a bundle. Thirdly, we propose a general frame to design 1 DOF deployable mechanism based on the continuation method. Three improvements in accuracy, speed, and generality are made. Feasible points of general and special N-side DGMs are calculated (3≤N≤7) based on plane-symmetric hexagon 6R and heptagon 7R mechanisms. Our results not only unify most deployable units but also design many new ones and reconfigurable DGMs. Fourthly, we propose the polyhedron net method and the least joint angle method to fold a polyhedron into a bundle and reduce the number of links, joints, and DOF. Many DPMs are designed.
... You and Chen [16], studied several types of deployable structures in which units are various mechanism types such as scissor-like elements, double-chain linkages, Bennett 4R or Bricard 6R linkages. Atarer et al. [17] designed several deployable network assemblies using the Altmann 6R linkage. The geometrical principles of various trusses in folding structures and the Sarrus mechanism are revealed in the study of Calatrava [18]. ...
The design of movable systems gives an opportunity to create transformable designs which respond to the environmental, functional, cultural, and aesthetical needs of today’s architecture. This paper proposes a method for designing a family of deployable structures which can be applied to semi-regular tessellated planar surfaces such as roofs, walls, and shading devices. The generated modular approach and adaptability provides a wide usage area and various combinations for these designs. The regular convex polygon modules are designed as a network of the triangular units. The triangular unit is designed using Bennett’s overconstrained plano-spherical linkage topology. The polygonal modules are assembled to each other in one-uniform semi-regular tessellations. The assembly of adjacent regular convex polygons in each tessellation is examined to find a proper solution for no collision during deployment and to properly fit a surface without any gaps or overlaps in the deployed position. The assembly method for creating 1-DoF deployable surfaces and mobility calculations for a unit, the polygonal modules, and the assemblies are computed, and motion studies are demonstrated with CAD models and exemplified for a square module for motion tests in a prototype.
... Their influence is often offset by the inflated accuracy of details manufacture, the performance of fitting operations during assembling, which leads to increase capital and operating costs. Sometimes the impact of redundant constraints occurs after repairs, which are usually accompanied by errors of surfaces shape and location due to low accuracy of tooling and assembling [1,13]. Methods for finding and eliminating redundant constraints is the basis for creating rational machine designs and reducing capital costs. ...
The structure of the MAK M43 diesel high pressure fuel pump driving is analyzed. It is shown that presence of redundant constraints in its mechanism is the reason of roller bearings failure. It is proposed redundant constraints elimination by adding movabilities in mechanism.
... Song et al. proposed a large-scale modular deployable mechanical network constructed by networking Altmann linkages [97]. Then, Korkmaz and Kiper constructed alternatives of network with several identical single-loop Altmann linkages [98], which have both fully deployed and folded configurations. ...
To overcome the problem that it is very difficult to analysis or design complicated 3D overconstrained linkages and their assemblies with conventional kinematic tools, this dissertation has proposed a novel truss method by applying structural theory to the truss form of 3D linkages to study their kinematic behaviours with the consideration of both the topology and geometry conditions. The method has also been adopted to analyse 3D overconstrained linkages and to design deployable polyhedrons. The major research findings are as follows.
First, the new truss method was developed, which converts 3D linkages to their corresponding truss forms while maintaining the kinematic behaviours. Under this method, mobility of complex linkages can be analysed by counting states of independent displacements with Maxwell’s rule. Besides that, their motion paths are able to be generated by the displacement updated algorithm based on singular value decomposition (SVD) of equilibrium matrix, and bifurcation position can hence be detected by recording singular values of equilibrium matrix during the motion process. The proposed method has been validated with planar 4R linkage, spherical 4R linkage, and threefold-symmetric Bricard linkage as examples.
Next, to eliminate strict overconstrained geometric conditions of linkages so that the tolerance of their fabrication error can be improved, the 3D overconstrained linkages are transformed into their corresponding truss forms. According to Maxwell’s rule and rank of the equilibrium matrix, the redundant bars in the truss form of the overconstrained linkage can be detected and removed to obtain a non-overconstrained linkage, while its kinematic equivalence is well kept. Adopting this method, the non-overconstrained forms of Bennett linkage and Myard 5R linkage have been found as RSSR linkage and RRSRR linkages, respectively. Furthermore, discussion on fabrication errors has been carried out to demonstrate the tolerance on the mobility and input-output curve of the non-overconstrained form.
And, polyhedral transformation has been realised by a kind of multi-loop linkages with complex topology, which enables large volumetric change amongst Platonic and Archimedean solids. Here, three sets of transformations have been proposed with their corresponding spatial linkages, namely truncated octahedron and cube, truncated tetrahedron and tetrahedron, as well as cuboctahedron and octahedron. Their constructions process and kinematic analysis were investigated in details by using the proposed truss method. Finally, motion analysis indicates that transformation paths are unique without singularity, which are further demonstrated with physical validation models. We envisage that our method could be extended to other paired polyhedrons.
Therefore, the truss method opens up a new way to analyse kinematics of 3D linkages. Meanwhile, the resultant non-overconstrained forms of overconstrained linkages and polyhedral transformations with one DOF are of great potential in engineering applications.
In this paper, the impact of parameter variations on the deployable motion characteristics, mobility, input singularity, and deploying/folding performance of plane-symmetric Bricard mechanisms is studied. Firstly, two classes of revolute pair axes used to construct deployable polygon mechanisms (DGMs) are reviewed, and their value ranges are further refined. Secondly, all possible axes arrangement schemes for plane-symmetric 6R DGMs are presented for the first time. Then, an improved schematic synthesis method is proposed, which can be used to design all plane-symmetric 6R DGMs that belong to the plane-symmetric Bricard mechanisms. Thirdly, the improved design method is applied to create a series of single-degree-of-freedom plane-symmetric 6R DGMs. Then, feasible domain searches are performed, and some of them are prototyped. Subsequently, the input singularity of plane-symmetric 6R DGMs is analyzed. Finally, two deploying/folding performance indices are proposed to evaluate the performance of plane-symmetric 6R DGMs with different fully deployed and fully folded states based on actual application scenarios. This work expands the variety and quantity of DGMs, which will also advance the development of robotics, mechanical metamaterials, and kirigami mechanisms.
The structure of steering gear’s HATLAPA mechanism is analyzed. It is shown that presence of redundant constraints in it increases laboriousness of gear montage and respectively worsen maintainability. On the basis of provided analysis developed mechanism with reduced more than twice redundant constrainsts number.
Стаття стосується найбільш поширеного типу суднових гідравлічних рульових машин (ГРМ) плунжерного типу, оснащених тангенсним важільним механізмом. Показано, що джерелом недоліків рульових машин плунжерного типу є недосконалість важільної системи, серед них зокрема її низький ККД, висока навантаженість деталей, та наявність значної кількості надлишкових зв’язків. Метою роботи є встановлення основних напрямків та оцінка резервів підвищення технічного рівня механізму ГРМ плунжерного типу. Задачі роботи полягають у наступному: визначити основні критерії технічного рівня механізму ГРМ плунжерного типу, що враховують досконалість структури, енергетичну ефективність його роботи, а також навантаженість деталей; виконати оцінку цих критеріїв для поширених конструкцій ГРМ плунжерного типу; намітити напрямки підвищення технічного рівня механізму ГРМ плунжерного типу та оцінити резерви їх застосування. Для розвантаження плунжерів та ущільнень гідроциліндрів від поперечних сил застосовують напрямні, які сполучаються з плунжерами нижчими кінематичними парами. Це забезпечує наявність в механізмі ГРМ q = 20 надлишкових зв'язків, що унеможливлюють самовстановлення ланок механізму. Резервом для зменшення кількості надлишкових зв'язків є відмова від напрямних та підвищення класу кінематичних пар механізму ГРМ. В результаті досліджень на прикладі машини прототипа YOOWON-MITSUBISHI YDFT-335-2 показано, що в ній забезпечується виникнення значних поперечних сил, що передаються від румпеля на плунжери та напрямні та сягають близько 53% від колових зусиль на румпелі. Для розвантаження плунжерів та ущільнень гідроциліндрів від поперечних сил застосовують напрямні, які здатні сприйняти лише 5...7% поперечного навантаження. Втрати на тертя плунжерів в ущільненнях серед усіх втрат на тертя в механізмі ГРМ складають 39%. Показано, що підвищення технічного рівня ГРМ, зокрема структурної досконалості, енергоощадності та зниження навантаженості деталей ГРМ має своїм ключем заміну тангенсного важільного механізму, що перетворює поступальний рух плунжерів в обертальних рух румпеля, на інший. Ключові слова: рульова машина плунжерного типу, плунжер, напрямна, румпель, момент, поперечна сила, розподіл навантаження, деформація, коефіцієнт корисної дії, структура.
Purpose. The article is aimed to carry out a structural analysis of gripping device as a mechanism with a variable structure and external unilateral constraints, as well as to determine the number of repeated connections in the internal and external contours in the mechanism diagram, and to recommend the ways to reduce them. Methodology. Solution of the set problem is realized by means of the mechanisms and machines theory using the universal structural theory of Ozols for analyzing the gripping device as a mechanism with internal and external constraints. Findings. The design of schemes of mechanical gripping devices rarely provides for a stage of structural analysis and synthesis of the mechanism. The preference is given to mandatory kinematic and kinetostatic calculations, layout and design. If structural analysis is carried out, then most often it is limited to calculating the number of the mechanism freedom degrees. The ten-link gripping device is built on the basis of coupled parallelogram slider-crank mechanism with a leading slider. The leading slider acts on the connecting rods connected by the rocker with the frame. The connecting rods bear the clamping elements of the gripping device. The added dyads form a parallelogram and provide a plane-parallel movement of the gripping elements of clamp. Structural analysis was performed using structural schemes for two states of the mechanism: before clamping the object and in the state of the clamped object. The main internal structural parameters of the kinematic scheme: the number of links - 10, the number of connections - 13, the number of contours - 4, the mobility - 1, the number of internal repeated connections - 11. The number of external connections - 12, the actual mobility of the mechanism - 1, the working mobility of the mechanism is - 0, the number of lost mobilities of the external body from the action of external connections - 6, the number of external repeated connections - 5. Originality. Structural analysis of the coupled slider crank mechanism of the gripping device as a mechanism of a variable structure with internal and external connections is carried out for the first time. It is performed contour search, analysis and elimination of useless repeated connections in the internal and external contours of the mechanism. Practical value. Practical recommendations for changing the mobility of kinematic pairs are proposed to reduce the number of repeated connections in internal contours and to provide unloading connection in the outer contour of the mechanism.
After introducing several basical concepts on Expandable Bar Structures and defining the patterns than can be used, a surveying on their applications as roofing is carried out. We propose expandable umbrellas which should be able for architectural purposes and discuses their constructional problems and analysis.
The research-prototype is a 4 x 5 x 2m, “topologically optimized” concrete shell that was designed and
built in ten days. The prototype and this ensuing paper aim to extend the rich legacy of form-finding to
adequately represent the complexities of scale, digital design systems and delivery mechanisms of contemporary architectural practice. They explore synergies in early design between architecture, structural engineering, and manufacturing.
During the last decades natural polymers have become more and more frequent to replace traditional inorganic stabilizers in building materials. The purpose of this research is to establish a comparison between the most conventional building material solutions for load-bearing walls and a type of biomaterial. This comparison will focus on load-bearing walls as used in a widespread type of twentieth century dwelling construction in Europe and still used in developing countries nowadays. To carry out this analysis, the structural and thermal insulation characteristics of different construction solutions are balanced. The tool used for this evaluation is the life cycle assessment throughout the whole lifespan of these buildings. This research aims to examine the environmental performance of each material assessed: fired clay brick masonry walls (BW), concrete block masonry walls (CW), and stabilized soil block masonry walls (SW) stabilized with natural fibers and alginates. These conventional and new materials are evaluated from the point of view of both operational and embodied energy.
Expandable space structures are of great value in situations where primary functional requirements include transportability and ease of erection. A family of expandable space structures are described in the present paper, where their practical applications and constructional aspects as well as their geometric and statical analyses are discussed.
This paper provides an overview of demountable connections and elements for steel and composite structures. Demountable connections are generally assembled from prefabricated structural members which can be reused after dismantling. This paper investigates innovative connections which enable steel and concrete framed structures to be made demountable. Demountable connections considered in this paper include beam-beam connections, column-column connections and beam-slab connectors. The finite element models for the nonlinear inelastic analysis of coped beams, column-column connections and composite beams are developed based on nonlinear finite element analysis techniques using the commercial finite element program, ABAQUS. The behaviours for coped steel beams and composite beams are then compared with the corresponding experimental results. The finite element models are used to investigate the effects of material and geometric properties on the behaviour of demountable connections. The finite element models can efficiently predict the plastic damage in the coped steel beam used in beam-beam connections. It is demonstrated that the coped beam can be made demountable up to a load of about 50% of the ultimate load which is greater than typical service loads. The computational results indicate that increasing the sleeve length and reinforcement ratio increases the stiffness and ultimate tensile strength of demountable column-column connections.
This paper presents a direct method for controlling nodal displacements, internal bar forces, and simultaneously both nodal displacements and internal bar forces, of a prestressable pin-jointed assembly under load. The method is aimed at static shape control of geometrically sensitive structures through length actuations in selected bars. The paper discusses identification of the most effective bars for actuation so that the desired shape can be obtained, without incurring violation in bar forces, through both a minimal number of actuators and minimum actuation in those actuators. The method can also be used for adjustment of bar forces to either reduce instances of high forces or increase low forces (e.g., in a cable nearing slack). © Copyright 2015 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
Latest Edition: 3D Printing and Additive Manufacturing: Principles and Applications (with Companion Media Pack). Fourth edition of Rapid Prototyping. Rapid prototyping (RP) has revolutionized how prototypes are made and small batch manufacturing is carried out. With rapid prototyping, the strategies used to produce a part change a number of important considerations and limitations previously faced by tool designers and engineers. Now in its third edition, this textbook is still the definitive text on RP. It covers the key RP processes, the available models and specifications, and their principles, materials, advantages and disadvantages. Examples of application areas in design, planning, manufacturing, biomedical engineering, art and architecture are also given. The book includes several related problems so that the reader can test his or her understanding of the topics. New to this edition, the included CD-ROM presents animated illustrations of the working principles of today’s key RP processes. © 2010 by World Scientific Publishing Co. Pte. Ltd. All rights reserved.