Experiments in fixturing mechanics

This paper describes an experimental fixturing system wherein fixel reaction forces, workpiece loading, and workpiece displacements are measured during simulated fixturing operations. The system's configuration, its measurement principles, and tests to characterize its performance are summarized. This system is used to experimentally determine the relationship between workpiece displacement and variations in fixed preload force or workpiece loading. We compare the results against standard theories, and conclude that commonly used linear spring models do not accurately predict workpiece displacements, while a non-linear compliance model provides better predictive behavior

Planar Ion Trap Geometry for Microfabrication

We describe a novel high aspect ratio radiofrequency linear ion trap geometry that is amenable to modern microfabrication techniques. The ion trap electrode structure consists of a pair of stacked conducting cantilevers resulting in confining fields that take the form of fringe fields from parallel plate capacitors. The confining potentials are modeled both analytically and numerically. This ion trap geometry may form the basis for large scale quantum computers or parallel quadrupole mass spectrometers. PACS: 39.25.+k, 03.67.Lx, 07.75.+h, 07.10+CmComment: 14 pages, 16 figure

On the optimal design of parallel robots taking into account their deformations and natural frequencies

This paper discusses the utility of using simple stiffness and vibrations models, based on the Jacobian matrix of a manipulator and only the rigidity of the actuators, whenever its geometry is optimised. In many works, these simplified models are used to propose optimal design of robots. However, the elasticity of the drive system is often negligible in comparison with the elasticity of the elements, especially in applications where high dynamic performances are needed. Therefore, the use of such a simplified model may lead to the creation of robots with long legs, which will be submitted to large bending and twisting deformations. This paper presents an example of manipulator for which it is preferable to use a complete stiffness or vibration model to obtain the most suitable design and shows that the use of simplified models can lead to mechanisms with poorer rigidity

Geometric Construction-Based Realization of Spatial Elastic Behaviors in Parallel and Serial Manipulators

This paper addresses the realization of spatial elastic behavior with a parallel or a serial manipulator. Necessary and sufficient conditions for a manipulator (either parallel or serial) to realize a specific elastic behavior are presented and interpreted in terms of the manipulator geometry. These conditions completely decouple the requirements on component elastic properties from the requirements on mechanism kinematics. New construction-based synthesis procedures for spatial elastic behaviors are developed. With these synthesis procedures, one can select each elastic component of a parallel (or serial) mechanism based on the geometry of a restricted space of allowable candidates. With each elastic component selected, the space of allowable candidates is further restricted. For each stage of the selection process, the geometry of the remaining allowable space is described

An Updating Method for Finite Element Models of Flexible-Link Mechanisms Based on an Equivalent Rigid-Link System

This paper proposes a comprehensive methodology to update dynamic models of flexible-link mechanisms (FLMs) modeled through ordinary differential equations. The aim is to correct mass, stiffness, and damping matrices of dynamic models, usually based on nominal and uncertain parameters, to accurately represent the main vibrational modes within the bandwidth of interest. Indeed, the availability of accurate models is a fundamental step for the synthesis of effective controllers, state observers, and optimized motion profiles, as those employed in modern control schemes. The method takes advantage of the system dynamic model formulated through finite elements and through the representation of the total motion as the sum of a large rigid-body motion and the elastic deformation. Model updating is not straightforward since the resulting model is nonlinear and its coordinates cannot be directly measured. Hence, the nonlinear model is linearized about an equilibrium point to compute the eigenstructure and to compare it with the results of experimental modal analysis. Once consistency between the model coordinates and the experimental data is obtained through a suitable transformation, model updating has been performed solving a constrained convex optimization problem. Constraints also include results from static tests. Some tools to improve the problem conditioning are also proposed in the formulation adopted, to handle large dimensional models and achieve reliable results. The method has been experimentally applied to a challenging system: a planar six-bar linkage manipulator. The results prove their capability to improve the model accuracy in terms of eigenfrequencies and mode shapes