Classification of direct kinematics to planar generalized Stewart platforms

AbstractThis paper presents the classification of direct kinematics for the planar generalized Stewart platform (GSP) which consists of two rigid bodies connected by three constraints between three pairs of points or lines in the base and the moving platforms. For each of the sixteen forms of planar GSPs, we give the explicit conditions on the parameters for the GSPs to have a given number of real solutions

Algorithms for detecting dependencies and rigid subsystems for CAD

Geometric constraint systems underly popular Computer Aided Design soft- ware. Automated approaches for detecting dependencies in a design are critical for developing robust solvers and providing informative user feedback, and we provide algorithms for two types of dependencies. First, we give a pebble game algorithm for detecting generic dependencies. Then, we focus on identifying the "special positions" of a design in which generically independent constraints become dependent. We present combinatorial algorithms for identifying subgraphs associated to factors of a particular polynomial, whose vanishing indicates a special position and resulting dependency. Further factoring in the Grassmann- Cayley algebra may allow a geometric interpretation giving conditions (e.g., "these two lines being parallel cause a dependency") determining the special position.Comment: 37 pages, 14 figures (v2 is an expanded version of an AGD'14 abstract based on v1

Real Coded Mixed Integer Genetic Algorithm for Geometry Optimization of Flight Simulator Mechanism Based on Rotary Stewart Platform

Featured Application Low-cost flight simulators with electric rotary actuators and optimized geometry for flight simulation. Designing the motion platform for the flight simulator is closely coupled with the particular aircraft's flight envelope. While in training, the pilot on the motion platform has to experience the same feeling as in the aircraft. That means that flight simulators need to simulate all flight cases and forces acting upon the pilot during flight. Among many existing mechanisms, parallel mechanisms based on the Stewart platform are suitable because they have six degrees of freedom. In this paper, a real coded mixed integer genetic algorithm (RCMIGA) is applied for geometry optimization of the Stewart platform with rotary actuators (6-RUS) to design a mechanism with appropriate physical limitations of workspace and motion performances. The chosen algorithm proved that it can find the best global solution with all imposed constraints. At the same time, the obtained geometry can be manufactured because integer solutions can be mapped to available discrete values. Geometry is defined with a minimum number of parameters that fully define the mechanism with all constraints. These geometric parameters are then optimized to obtain custom-tailored geometry for aircraft flight simulation

Symmetric Subspace Motion Generators

When moving an object endowed with continuous symmetry, an ambiguity arises in its underlying rigid body transformation, induced by the arbitrariness of the portion of motion that does not change the overall body shape. The functional redundancy caused by continuous symmetry is ubiquitously present in a broad range of robotic applications, including robot machining and haptic interface (revolute symmetry), remote center of motion devices for minimal invasive surgery (line symmetry), and motion modules for hyperredundant robots (plane symmetry). In this paper, we argue that such functional redundancy can be systematically resolved by resorting to symmetric subspaces (SSs) of the special Euclidean group SE(3), which motivates us to systematically investigate the structural synthesis of SS motion generators. In particular, we develop a general synthesis procedure that allows us to generate a wide spectrum of novel mechanisms for use in the applications mentioned

Using the FRDPARRC design methodology to drive innovation in the HETDEX PFIP support adjustable strut assembly

textThis thesis provides background information on the Hobby-Eberly Telescope (HET), HET Dark Energy Experiment (HETDEX), Gough-Stewart platforms (GSP), the Prime Focus Instrument Package (PFIP) support structure, and the design methodology used to design said support structure. Each component is analyzed from the point of view of Professor Alex Slocum’s FRDPARRC design methodology. Each aspect of the design is shown to have been derived by following the steps of Slocum’s design method. Material selection, manufacturing techniques, and integration of off-the-shelf components into the support system are also discussed in reference to FRDPARRC. The assembly procedure for the PFIP structure is outlined. Finally, using specific examples from the detailed design, the FRDPARRC method itself is analyzed and its ability to drive innovation in design is evaluated.Mechanical Engineerin

Controlo e execução de estampagem incremental com cinemática paralela

Mestrado em Engenharia MecânicaO projeto SPIF-A é um verdadeiro desa o de engenharia: desenvolver uma má- quina totalmente nova e inovadora para conformação plástica de chapa. Trata-se principalmente de um trabalho de equipa, que abrange varias áreas da engenharia mecânica, desde análise estrutural até automação e controlo, passando pela termodin âmica e cinemática, entre outras. Esta dissertação sendo mais uma peça no puzzle, vai-se focar no seu desenvolvimento, principalmente no estudo da cinemática inversa e directa da plataforma de Stewart, assim como no desenvolvimento do primeiro sistema de controlo de posição. O referido sistema é um controlador de lógica difusa e será implementado através de software num computador de processamento em tempo real. Durante o desenvolvimento destes componentes também foram optimizados e/ou actualizados os sistemas hidráulicos, eléctricos e mecânicos da máquina assim como se implementou e calibrou um sistema de medição de forças de trabalho recorrendo ao uso de células de carga.The SPIF-A project is a true engineering challenge: to develop an entirely new and innovative machine for sheet metal forming. It is mostly a team e ort, covering various engineering subjects from structural analysis to automation and control but also thermodynamics, kinematics, among others. This dissertation being another piece of that puzzle, will focus on machine development, namely on de ning the machine's Stewart platform inverse kinematics, proposing a solution for the forward kinematics and devising its rst position control system. The referred system will be a fuzzy logic controller and will be implemented via software on a real time targeting machine. During this work several components like from its hydraulic, electrical and mechanical systems were updated and a force measuring system, using load cells was installed and calibrated

Type Synthesis and Performance Optimization of Parallel Manipulators

Parallel robots have been widely employed in industrial applications. There are still some challenging topics in the fundamental research, e.g., the primary problem mobility analysis has not been solved for about 150 years. A universal mobility equation for all kinds of parallel architectures has not been found. Another issue lies on the performance measurements for parallel manipulators. There are plenty of kinematic and dynamic performance indices. However, the various ranges and scales of these indicators make the optimal design considering multiple indices complicated. It is essential to search for a unified approach to normalize performance indicators. More dynamic performance measurement indicators should be raised to explore the dynamic features and complete the theory for parallel mechanisms. In this research, an improved mobility equation is designed to reveal the degrees of freedom for a special class of parallel robots. A novel methodology called the kinematic joint matrix is proposed. It possesses the mapping relations with parallel manipulators. A series of 2-6 degrees of freedom parallel architectures is denoted by the kinematic joint matrix. The theory of screw is employed to check the feasibility from several kinds of parallel structures. A special block diagram is introduced to distinguish various kinematic joint matrices. Since this family of parallel robots contains various motion characteristics, four parallel robots with distinct features are selected. Based on the kinematic models, three categories of singularities are explored. The operational and reachable workspaces of the pure-translational parallel robots are searched and the parametric analyses are reported. The linkage’s impacts for the reachable workspace of the mixed-motion parallel architectures are investigated. The novel performance level index is designed to unify the positive performance index and demonstrated the performance rank for any pose (position and orientation). The dexterity index is utilized as an example to verify the characteristics of the level index. The distributions and parametric analyses of two novel mass-related performances are studied. The dimension synthesis of a selected planar parallel robot is presented based on the non-dominated genetic algorithm II. The experiment results testify the correctness of the mobility and kinematic mathematical models of this mechanism