Topology and Constraint Analysis of Reconfiguration in Metamorphic Mechanisms

This paper investigates the reconfiguration of the metamorphic mechanisms and proposes mechanism topology matrix, phase matrix and augmented adjacency matrix to identify variation of geometric and topological configurations. This is then used to investigate the two generic ways in the study of induced constraint change of the metamorphic mechanisms. The topological phase change of the metamorphic mechanisms correlative to the variable-axis revolute joints and link annex is hence investigated and constraint analysis is then presented in the working phases of the new metamorphic mechanisms.

Potential of the 3-UPU Translational Parallel Manipulator

The 3-UPU three degrees of freedom fully parallel manipulator, where U and P are for universal and prismatic pair respectively, is a very well known manipulator that can provide the platform with three degrees of freedom of pure translation, pure rotation or mixed translation and rotation according to the relative directions of the revolute axes. Many studies have been reported in the literature on singularities, workspace and joint clearance influence on the platform accuracy of this manipulator. However, much work has still to be done to reveal all the features this topology can offer to the designer. This paper collects the previous most relevant work done on the 3-UPU parallel manipulator and shows the main results in a coherent general frame. The paper proposes new architectures of the 3-UPU manipulator which offer interesting features to the designer. Finally, based on a number of indexes, a procedure is proposed that allows the designer to select the best architecture of the 3-UPU manipulator for a given task.

Nonlinear Constraint Model for Symmetric Three-Dimensional Beams

The constraint-based design of flexure mechanisms requires a qualitative and quantitative understanding of the constraint characteristics of flexure elements that serve as constraints. This paper presents the constraint characterization of a slender, uniform and symmetric cross-section, spatial beam, which is one of the most basic flexure elements used in three-dimensional flexure mechanisms. The constraint characteristics of interest, namely stiffness and error motions, are determined from the non-linear load-displacement relations of the beam. Appropriate simplifying assumptions are made in deriving these relations so that relevant non-linear effects (load-stiffening, kinematic, and elastokinematic) are captured in a compact, closed-form, and parametric manner. The resulting spatial beam constraint model is shown to be accurate, using non-linear finite element analysis, within a load and displacement range of practical interest. The utility of this model lies in the physical and analytical insight that it offers into the constraint behavior of a spatial beam flexure, its use in 3D flexure mechanism geometries, and fundamental performance tradeoffs in flexure mechanism design.

Screw Systems Generated From Subalgebras: Properties and Applications

The contribution presents the properties and applications of screw systems generated from the addition of subalgebras of the Lie algebra, se(3), of the Euclidean group, SE(3). It is shown that these screw systems have important properties related with the mobility of kinematic chains formed with these screw systems.

Geometric, Spatial Path Tracking Using Non-Redundant Manipulators via Speed-Ratio Control

Path tracking can be accomplished by separating the control of the desired trajectory geometry and the control of the path variable. Existing methods accomplish tracking of up to third-order geometric properties of planar paths and up to second-order properties of spatial paths using non-redundant manipulators, but only in special cases. This paper presents a novel methodology that enables the geometric tracking of a desired planar or spatial path to any order with any non-redundant regional manipulator. The governing first-order coordination equation for a spatial path-tracking problem is developed, the repeated differentiation of which generates the coordination equation of the desired order. In contrast to previous work, the equations are developed in a fixed global frame rather than a configuration-dependent canonical frame, providing a significant practical advantage. The equations are shown to be linear, and therefore, computationally efficient. As an example, the results are applied to a spatial 3-revolute mechanism that tracks a spatial path. Spatial, rigid-body guidance is achieved by applying the technique to three points on the end-effector of a six degree-of-freedom robot. A spatial 6-revolute robot is used as an illustration.

Kinematic-, Static- and Workspace Analysis of a 6-P-U-S Parallel Manipulator

This paper examines the symbolic kinematic modeling of a general 6-P-U-S (prismatic-universal-spherical) parallel kinematic manipulator (PKM). The base location of actuators has been previously shown to lead to: (i) reduction of the (motor) weight carried by the legs; (ii) elimination of the actuation transmission requirement (through intermediary joints as in the case of the Stewart-Gough platform); and (iii) most-importantly absorption of reaction-forces by the ground. We focus on using the symbolic equations to derive the conditions for type I and II singularities of this class of parallel manipulators. Based on these conditions, this system of equations is specialized to a specific configuration of the platform that has superior structural design and comparatively minimal singularities within its workspace. A series of studies were conducted to investigate the quality of workspace as well as estimate the actuation requirements for a unit payload carried over their workspace using the symbolic Jacobian model for this specialized configuration.

Design and Fabrication of a Multi-Material Compliant Flapping Wing Drive Mechanism for Miniature Air Vehicles

Successful realization of a flapping wing micro air vehicle (MAV) requires development of a light weight drive mechanism converting the rotary motion of the motor into flapping motion of the wings. Low weight of the drive mechanism is required to maximize the payload and battery capacity. In order to make flapping wing MAVs attractive in search, rescue, and recovery missions, they should be disposable from the cost point of view. Injection molded compliant drive mechanisms are an attractive design option to satisfy the weight, efficiency and cost requirements. In the past, we have successfully used multi-piece molding to create mechanisms utilizing distributed compliance for smaller MAVs. However, as the size of the MAV increases, mechanisms with distributed compliance exhibit excessive deformation. Therefore localizing rather than distributing the compliance in the mechanism becomes a more attractive option. Local compliance can be realized through multimaterial designs. A multi-material injection molded mechanism additionally offers reduction in the number of parts. This paper describes an approach for determining the drive mechanism shape and size that meets both the functional design and multi-material molding requirements. The design generated by the approach described in this paper was utilized to realize a flapping wing MAV with significant enhancements in the payload capabilities.

Developing a Kinematic Estimation Model for a Climbing Mobile Robotic Welding System

Skid steer tracked-based robots are popular due to their mechanical simplicity, zero-turning radius and greater traction. This architecture also has several advantages when employed by mobile platforms designed to climb and navigate ferrous surfaces, such as increased magnet density and low profile (center of gravity). However, creating a kinematic model for localization and motion control of this architecture is complicated due to the fact that tracks necessarily slip and do not roll. Such a model could be based on a heuristic representation, an experimentally-based characterization or a probabilistic form. This paper will extend an experimentally-based kinematic equivalence model to a climbing, track-based robot platform. The model will be adapted to account for the unique mobility characteristics associated with climbing. The accuracy of the model will be evaluated in several representative tasks. Application of this model to a climbing mobile robotic welding system (MRWS) is presented.

Achieving Multistability Through Use of a Single Bistable Compliant Mechanism

A compliant multistable mechanism is capable of steadily staying at multiple distinct positions without power input. Many applications including switches, valves, relays, positioners, and reconfigurable robots may benefit from multistability. In this paper, two new approaches for synthesizing compliant multistable mechanisms are proposed, which enable designers to achieve multistability through the use of a single bistable mechanism. The synthesis approaches are described and illustrated by several design examples. Compound use of both approaches is also discussed. The design potential of the synthesis approaches is demonstrated by the successful operation of several instantiations of designs that exhibit three, four, five, and nine stable equilibrium positions, respectively. The synthesis approaches enable us to design a compliant mechanism with a desired number of stable positions.

Design of a Generic Zero Stiffness Compliant Joint

The objective of this paper is to design a generic zero stiffness compliant joint. This compliant joint could be used as a generic construction element in a compliant mechanism. To avoid the spring-back behavior of conventional compliant joints, the principle of static balancing is applied, implying that for each position of the joint the total potential energy should be constant. To this end, a conventional balanced mechanism, consisting of two pivoted bodies which are balanced with two zero-free-length springs, is taken as an initial concept. The joint is replaced by a compliant cross-axis flexural pivot and each spring is replaced by a pair of compliant leaf springs. For both parts an analytic model was implemented and a configuration with the lowest energy fluctuation was found through optimization. A FEA model was used to verify the analytic model of the optimized design. A prototype was manufactured and tested. Both the FEA model and the experiment confirm the reduction of the needed moment to rotate the compliant joint. The experiment shows the balanced compliant joint is not completely balanced but the moment required to rotate the joint is reduced by 70%. Thus, a statically balanced compliant generic joint element was designed which bears great promise in designing statically balanced compliant mechanisms and making this accessible to any designer.