Optimum Synthesis and Design of a Hood Linkage for Static Balancing in One-Step

The conventional approach of the mechanism design process, generally, has a two-step procedure: Kinematic synthesis/analysis of the mechanism in the first step and optimization of the synthesized/analyzed mechanism based on optimization criteria in the second step. This study presents an approach that combines kinematic synthesis with the static balancing of the same, and optimization, into a one-step procedure. As an example of this one-step design process, a tension-spring assisted four-bar hood linkage optimal synthesis and design is performed in one-step. This one-step solution includes kinematic synthesis and analysis of the hood linkage, virtual work, static balancing with tension spring, and optimization in the presence of joint friction. The resulting design requires a minimum force to raise and lower the hood in the presence of unknown optimum levels of joint friction while the hood is statically balanced for its entire range of motion. A total of twelve different scenarios are investigated and the results are discussed

Optimal Design of Beam-Based Compliant Mechanisms via Integrated Modeling Frameworks

Beam-based Compliant Mechanisms (CMs) are increasingly studied and implemented in precision engineering due to their advantages over the classic rigid-body mechanisms, such as scalability and reduced need for maintenance. Straight beams with uniform cross section are the basic modules in several concepts, and can be analyzed with a large variety of techniques, such as Euler-Bernoulli beam theory, Pseudo-Rigid Body (PRB) method, chain algorithms (e.g.~the Chained Beam-Constraint Model, CBCM) and Finite Element Analysis (FEA). This variety is unquestionably reduced for problems involving special geometries, such as curved or spline beams, variable section beams, nontrivial shapes and, eventually, contacts between bodies. 3D FEA (solid elements) can provide excellent results but the solutions require high computational times. This work compares the characteristics of modern and computationally efficient modeling techniques (1D FEA, PRB method and CBCM), focusing on their applicability in nonstandard problems. In parallel, as an attempt to provide an easy-to-use environment for CM analysis and design, a multi-purpose tool comprising Matlab and modern Computer-Aided Design/Engineering (CAD/CAE) packages is presented. The framework can implement different solvers depending on the adopted behavioral models. Summary tables are reported to guide the designers in the selection of the most appropriate technique and software architecture. The second part of this work reports demonstrative case studies involving either complex shapes of the flexible members or contacts between the members. To improve the clarity, each example has been accurately defined so as to present a specific set of features, which leads in the choice of a technique rather than others. When available, theoretical models are provided for supporting the design studies, which are solved using optimization approaches. Software implementations are discussed throughout the thesis. Starting from previous works found in the literature, this research introduces novel concepts in the fields of constant force CMs and statically balanced CMs. Finally, it provides a first formulation for modeling mutual contacts with the CBCM. For validation purposes, the majority of the computed behaviors are compared with experimental data, obtained from purposely designed test rigs

Geometry-based structural analysis and design via discrete stress functions

This PhD thesis proposes a direct and unified method for generating global static equilibrium for 2D and 3D reciprocal form and force diagrams based on reciprocal discrete stress functions. This research combines and reinterprets knowledge from Maxwell’s 19th century graphic statics, projective geometry and rigidity theory to provide an interactive design and analysis framework through which information about designed structural performance can be geometrically encoded in the form of the characteristics of the stress function. This method results in novel, intuitive design and analysis freedoms. In contrast to contemporary computational frameworks, this method is direct and analytical. In this way, there is no need for iteration, the designer operates by default within the equilibrium space and the mathematically elegant nature of this framework results in its wide applicability as well as in added educational value. Moreover, it provides the designers with the agility to start from any one of the four interlinked reciprocal objects (form diagram, force diagram, corresponding stress functions). This method has the potential to be applied in a wide range of case studies and fields. Specifically, it leads to the design, analysis and load-path optimisation of tension-and compression 2D and 3D trusses, tensegrities, the exoskeletons of towers, and in conjunction with force density, to tension-and-compression grid-shells, shells and vaults. Moreover, the abstract nature of this method leads to wide cross-disciplinary applicability, such as 2D and 3D discrete stress fields in structural concrete and to a geometrical interpretation of yield line theory

Type synthesis and static balancing of a class of deployable mechanisms

This thesis addresses the type synthesis and static balancing of a class of deployable mechanisms, which can be applied in applications in many areas including aerospace and daily life. Novel construction methods are proposed to obtain the deployable mechanisms. First, the type synthesis of the foldable 8-revolute joint (R) linkages with multiple modes is presented. Two types of linkages are constructed by connecting planar 4R linkages and spherical 4R linkages. The obtained linkages can be folded into two layers or four layers, and have multiple motion modes. A spatial triad is also adopted to build single-loop linkages, then the single-loop linkages are connected using spherical (S) joints or RRR chains to obtain deployable polyhedral mechanisms (DPMs). The DPMs have only 1- degree-of-freedom (DOF) when deployed, and several mechanisms with 8R linkages and 10R linkages have multiple motion modes and can switch modes through transition positions. In addition, when connecting single-loop linkages using half the number of the RRR chains, the prism mechanisms obtain an additional 1-DOF rotation mode. Furthermore, the DPMs are developed into statically balanced mechanisms. The geometric static balancing approaches for the planar 4R parallelogram linkages, planar manipulators, spherical manipulators and spatial manipulators are developed so that the mechanisms can counter gravity while maintaining the positions of the mechanisms. Only springs are used to design the statically balanced system readily, with almost no calculation. A novel numerical optimization approach is also introduced which adopts the sum of squared differences of the potential energies as the objective function. Using the proposed static balancing approaches, the 8R linkages and the DPMs presented in this thesis can be statically balanced

Kinematics and stiffness of a planar tensegrity parallel mechanism

In this work, the kinematics and stiffness of a planar tensegrity parallel mechanism are investigated. The analytical solutions to the forward and reverse kinematics were found using an energy method. The singular configurations and workspaces were detailed. Afterwards, the stiffness of the mechanism was analyzed. It is demonstrated that the stiffness is at a local maximum when the mechanism is in stable equilibrium and at a local minimum when the mechanism is in unstable equilibrium. The stiffness distributions are approximately symmetric about a certain line inside the actuator and Cartesian workspaces. Large values of the actuator length should be selected for high stiffness applications. The singular configurations, workspaces and stiffness variations inside the actuator and Cartesian workspaces lay a foundation for the use of the mechanism

Modelling and Experimental Evaluation of a Static Balancing Technique for a new Horizontally Mounted 3-UPU Parallel Mechanism

This paper presents the modelling and experimental evaluation of the gravity compensation of a horizontal 3-UPU parallel mechanism. The conventional Newton-Euler method for static analysis and balancing of mechanisms works for serial robots; however, it can become computationally expensive when applied to the analysis of parallel manipulators. To overcome this difficulty, in this paper we propose an approach, based on a Lagrangian method, that is more efficient in terms of computation time. The derivation of the gravity compensation model is based on the analytical computation of the total potential energy of the system at each position of the end-effector. In order to satisfy the gravity compensation condition, the total potential energy of the system should remain constant for all of the manipulator's configurations. Analytical and mechanical gravity compensation is taken into account, and the set of conditions and the system of springs are defined. Finally, employing a virtual reality environment, some experiments are carried out and the reliability and feasibility of the proposed model are evaluated in the presence and absence of the elastic components

Dynamic balance and walking control of biped mechanisms

The research presented here focuses on the development of a feedback control systems for locomotion of two and three dimensional, dynamically balanced, biped mechanisms. The main areas to be discussed are: development of equations of motion for multibody systems, balancing control, walking cycle generation, and interactive computer graphics. Additional topics include: optimization, interface devices, manual control methods, and ground contact force generation;Planar (2D) and spatial (3D) multibody system models are developed in this thesis to handle all allowable ground support conditions without system reconfiguration. All models consist of lower body segments only; head and arm segments are not included. Model parameters for segment length, mass, and moments of inertia are adjustable. A ground contact foot model simulates compression compliance and allows for non-uniform surfaces. In addition to flat surfaces with variable friction coefficients, the systems can adapt to inclines and steps;Control techniques are developed that range from manual torque input to automatic control for several types of balancing, walking, and transitioning modes. Balancing mode control algorithms can deal with several types of initial conditions which include falling and jumping onto various types of surfaces. Walking control state machines allow selection of steady-state velocity, step size, and/or step frequency;The real-time interactive simulation software developed during this project allows the user to operate the biped systems within a 3D virtual environment. In addition to presenting algorithms for interactive biped locomotion control, insights can also be drawn from this work into the levels of required user effort for tasks involving systems controlled by simultaneous user inputs;Position and ground reaction force data obtained from human walking studies are compared to walking data generated by one of the more complex biped models developed for this project

Kinematics for Combined Quasi-Static Force and Motion Control in Multi-Limbed Robots

This paper considers how a multi-limbed robot can carry out manipulation tasks involving simultaneous and compatible end-effector velocity and force goals, while also maintaining quasi-static stance stability. The formulation marries a local optimization process with an assumption of a compliant model of the environment. For purposes of illustration, we first develop the formulation for a single fixed based manipulator arm. Some of the basic kinematic variables we previously introduced for multi-limbed robot mechanism analysis in [1] are extended to accommodate this new formulation. Using these extensions, we provide a novel definition for static equilibrium of multi-limbed robot with actuator limits, and provide general conditions that guarantee the ability to apply arbitrary end-effector forces. Using these extended definitions, we present the local optimization problem and its solution for combined manipulation and stance. We also develop, using the theory of strong alternatives, a new definition and a computable test for quasi-static stance feasibility in the presence of manipulation forces. Simulations illustrate the concepts and method