Clasificación de sistemas de helicoides para el diseño de mecanismos tridimensionales y robots

El Grupo de Lie SE(3), denominado grupo Especial Euclideano de los desplazamientos tridimensionales, se ha utilizado intensivamente para el análisis de mecanismos, robots y sistemas multicuerpo. En cambio, para la síntesis y el diseño conceptual de mecanismos en tres dimensiones se han utilizado helicoides, que son elementos del álgebra de Lie se(3). Los helicoides son una representación matemática muy utilizada para describir el movimiento tridimensional acoplado en traslación y rotación. En este trabajo se describe una clasificación exhaustiva de sistemas de helicoides infinitesimales disponible en la literatura y se aportan ejemplos de cada sistema y de la intersección de los sistemas con sus espacios recíprocos. En trabajos futuros, estos sistemas se utilizarán como base de datos para el diseño automático de mecanismos y robots.Publicado en: Mecánica Computacional vol. XXXV, no. 20Facultad de Ingenierí

Clasificación de sistemas de helicoides para el diseño de mecanismos tridimensionales y robots

El Grupo de Lie SE(3), denominado grupo Especial Euclideano de los desplazamientos tridimensionales, se ha utilizado intensivamente para el análisis de mecanismos, robots y sistemas multicuerpo. En cambio, para la síntesis y el diseño conceptual de mecanismos en tres dimensiones se han utilizado helicoides, que son elementos del álgebra de Lie se(3). Los helicoides son una representación matemática muy utilizada para describir el movimiento tridimensional acoplado en traslación y rotación. En este trabajo se describe una clasificación exhaustiva de sistemas de helicoides infinitesimales disponible en la literatura y se aportan ejemplos de cada sistema y de la intersección de los sistemas con sus espacios recíprocos. En trabajos futuros, estos sistemas se utilizarán como base de datos para el diseño automático de mecanismos y robots.Publicado en: Mecánica Computacional vol. XXXV, no. 20Facultad de Ingenierí

Clasificación de sistemas de helicoides para el diseño de mecanismos tridimensionales y robots

El Grupo de Lie SE(3), denominado grupo Especial Euclideano de los desplazamientos tridimensionales, se ha utilizado intensivamente para el análisis de mecanismos, robots y sistemas multicuerpo. En cambio, para la síntesis y el diseño conceptual de mecanismos en tres dimensiones se han utilizado helicoides, que son elementos del álgebra de Lie se(3). Los helicoides son una representación matemática muy utilizada para describir el movimiento tridimensional acoplado en traslación y rotación. En este trabajo se describe una clasificación exhaustiva de sistemas de helicoides infinitesimales disponible en la literatura y se aportan ejemplos de cada sistema y de la intersección de los sistemas con sus espacios recíprocos. En trabajos futuros, estos sistemas se utilizarán como base de datos para el diseño automático de mecanismos y robots.Publicado en: Mecánica Computacional vol. XXXV, no. 20Facultad de Ingenierí

An Overview of Formulae for the Higher-Order Kinematics of Lower-Pair Chains with Applications in Robotics and Mechanism Theory

The motions of mechanisms can be described in terms of screw coordinates by means of an exponential mapping. The product of exponentials (POE) describes the configuration of a chain of bodies connected by lower pair joints. The kinematics is thus given in terms of joint screws. The POE serves to express loop constraints for mechanisms as well as the forward kinematics of serial manipulators. Besides the compact formulations, the POE gives rise to purely algebraic relations for derivatives wrt. joint variables. It is known that the partial derivatives of the instantaneous joint screws (columns of the geometric Jacobian) are determined by Lie brackets the joint screws. Lesser-known is that derivative of arbitrary order can be compactly expressed by Lie brackets. This has significance for higher-order forward/inverse kinematics and dynamics of robots and multibody systems. Various relations were reported but are scattered in the literature and insufficiently recognized. This paper aims to provide a comprehensive overview of the relevant relations. Its original contributions are closed form and recursive relations for higher-order derivatives and Taylor expansions of various kinematic relations. Their application to kinematic control and dynamics of robotic manipulators and multibody systems is discussed

Mechanologic: Designing Mechanical Devices that Compute

Despite their initial success and impact on the development of the modern computer, mechanical computers were quickly replaced once electronic computers became viable. Recently, there has been increased interest in designing devices that compute using modern and unconventional materials. In this dissertation, we investigate multiple ways to realize a mechanical device that can compute, with a main focus on designing mechanical equivalents for wires and transistors. For our first approach at designing mechanical wires, we present results on the propagation of signals in a soft mechanical wire composed of bistable elements. When we send a signal along bistable wires that do not support infinite signal propagation, we find that signals can propagate for a finite distance controlled by a penetration length for perturbations. We map out various parameters for this to occur, and present results from experiments on wires made of soft elastomers. Our second approach for designing mechanical devices that compute focuses on designing the topology of the configuration space of a linkage. By programming the configuration space through small perturbations of the bar lengths in the linkage, we are able to design a linkage that gates the propagation of a soliton in a Kane-Lubensky chain. This dissertation also includes other results related to the study of small length changes in linkages and an analysis of a version of a mechanical transistor compatible with the soft bistable wires

When to Hold and When to Fold: Studies on the topology of origami and linkages

Linkages and mechanisms are pervasive in physics and engineering as models for avariety of structures and systems, from jamming to biomechanics. With the increasein physical realizations of discrete shape-changing materials, such as metamaterials,programmable materials, and self-actuating structures, an increased understandingof mechanisms and how they can be designed is crucial. At a basic level, linkagesor mechanisms can be understood to be rigid bars connected at pivots around whichthey can rotate freely. We will have a particular focus on origami-like materials, anextension to linkages with the added constraint of faces. Self-actuated versions typ-ically start flat and when exposed to an external stimulus - such as a temperaturechange or magnetic field - spontaneously fold. Since these structures fold all at once,and the number of folding patterns accessible to a given origami are exponential, theyare prone to folding to a configuration other than the desired one. Other work hassuggested methods for avoiding this misfolding, but it assumes ideal, rigid origami. Here, we expand on these models to account for the elasticity of real structures andintroduce methods for accounting for Gaussian curvature in them. We also explorehow to find and set an upper bound on minimal forcing sets, or the minimum set offolds required to force an origami, and present a graph theory algorithm for findingthem in arbitrary origami. Taken altogether, these origami studies give insight intohow the physical properties of origami influence folding and a new set of tools foravoiding misfolding. Next, we turn back to a more fundamental study of linkagesand present a new method for finding the manifold of their critical points. We thendemonstrate a design protocol that utilizes this manifold to create linkages with tun-able motions, before turning to several example structures, including the four-barlinkage and the Kane-Lubensky chain