Mathematical Model for Large Deflection Dynamics of a Compliant Beam Mechanism

A mathematical model for the large deflection dynamics of a compliant beam mechanism is presented. The mechanism simulates the motion of a slider-crank device. The system contains a highly flexible beam that provides the compliant motion from a sliding mass at one end to a rotating hinge point at the other end. Basic models for friction and beam dissipation effects are included. Principles of mechanics are used to derive a nonlinear integro-partial differential equation for the complete beam/mass system in the curved space of the deformed beam. The resulting equation is cast into a generalized nondimensional form suitable for studying system behavior for a broad range of system sizes. The dynamic equation is solved in curved space by applying a spatial solution that closely represents the large deflection measured static deflection of the beam. The nonlinear system dynamics are simulated for an initial large deflection of the mechanism and compared to experimental results for an actual physical system.

Real Continuation Method and its Application in Kinematic Synthesis

Real continuation method for finding real solutions to non-linear equations is proposed. Synthesis of planar four-bar linkage for path generation with nine precision points is studied using this method. The proposed method has high efficiency and can best be used for solving synthesis problems.

On the Comparison of the Pseudo Rigid Body Model Method and the Finite Element Method for a 3DOF Planar Micro-Motion Stage

This paper discusses one type of commonly used parallel manipulator mechanism for the generation of micro-motion. This mechanism is designed as a compliant mechanism. The design and control of such a compliant mechanism is an important issue. This paper focuses on kinematic issues with consideration of future real-time control of the system. In particular, a constant-Jacobian method to approximate the kinematics, which is based on a pseudo rigid body model of the compliant mechanism, is further validated. This validation is based on the difference between this approximate method and the finite element method to the actual device, for an actuator range of 0–15 μm. The computational time with this approximate method is nearly 50 times less than that with the finite element method. It is expected that this approximation method will be far superior to the finite element method in terms of real-time control.

Comparison of Damped Velocity and Acceleration Control for Non-Redundant Manipulators

Damped Least Square (DLS) method has been widely used as an on-line algorithm for manipulator path tracking near and at singular configurations. Wampler (1986) formulated the framework of DLS method applied to velocity control and addressed the applicability of DLS method to acceleration control. The purpose of this paper is to demonstrate the differences in the joint paths generated by damped velocity and damped acceleration control algorithms in non-redundant manipulators. We examine these joint paths, find the cause of the differences, and demonstrate the features of damped acceleration control in non-redundant manipulator dynamics. Simulation results on a planar 2R and a spatial 6R manipulator moving through and near singular configurations verify the phenomena analyzed.

Finite Element Analysis of Circular Wedge Connections

In this paper, the finite element analysis of circular wedge connections is described, and conclusions for the performance of the connection are derived. In the foreground of the examinations are stresses and deformations while tightening of the connection. Starting with the general structural performance, the influences on power transmission like slope, number of wedges, coefficient of sliding friction and outer hub diameter are discussed. An analytic function to describe the gap pressure within the tightened joint is introduced and rates to explain the problem of centering of circular wedge connections are shown. Finally two concepts for dimensioning are presented and recommendations for application of this connection are given.

Dynamic Modeling and Analysis of a Two D.O.F. Mobile Manipulator

This paper presents the kinematic and dynamic modeling of a two degrees of freedom manipulator attached to a vehicle with a two degrees of freedom suspension system. The vehicle is considered to move with a constant linear speed over an irregular ground-surface while the end-effector tracks a desired trajectory in a fixed reference frame. In addition, the effects of highly coupled dynamic interaction between the manipulator and vehicle (including the suspension system’s effects) have been studied. Finally, simulation results for the end-effector’s straight-line trajectory are presented to illustrate these effects.

Design of Actuator Endurance and Reliability Testbed

This paper presents a novel test bed devised for the testing of various types of next generation robot actuators, especially modular actuators. Requirements for actuator tests are different from motor testing because actuators for robotic application are highly unique and specialized devices with numerous parameters and conditions to be considered. To meet the high demand of a particular application, the actuator must be carefully tested using highly advanced measurement equipment. The first section introduces the 4-test bed suite for the evaluation environment of modern actuators with their purposes and measurement parameters. General information on the performance testing of actuators is also given. The hardware and software environment of the Actuator Endurance and Reliability Test Bed (AERTB) is then described in depth. Preliminary tests have been done to verify and check the proper operation of the test bed. Test results show that the developed test bed offers excellent testing capability of robot actuators with ease of use.

Design, Simulation and SFF Techniques for Functional Components

Development of Solid Freeform Fabrication (SFF) systems has created the opportunity for new approaches in design of functional components, which leverages the inherent strengths of both experiment and numerical simulation. This paper describes an approach in which the computational models are integrated with the rapid prototyping fabrication processes. The parts are fabricated using different materials including wax, PZT, silicone nitride, and 17-4PH stainless steel powders for the SFF hardware (Langrana et al, 2000, Qiu et al, 1999, Danforth et al, 1998) and Ciba-Geigy SL-resin for SLA hardware (Higgins and Langrana, 1998, Higgins and Langrana 1999). The components such as turbine blades, actuators, and fixtures have been designed, simulated and fabricated. The properties of parts have been and are being quantified in terms of accuracy and quality.

Rapid Prototyping of Lower-Pair, Geared-Pair and Cam Mechanisms

In this paper, a framework for the rapid prototyping of lower-pair, geared-pair and cam mechanisms using a commercially available CAD package and a Fused Deposition Modeling (FDM) rapid prototyping machine is presented. A database of lower kinematic pairs (joints) is developed experimentally. Geared-pair and cam mechanisms are also developed. These mechanisms are then used in the design of the prototypes. Examples are presented in order to demonstrate the potential of this technique. Physical prototypes can be of great help in the design of mechanisms by allowing the 3D visualization of the mechanism as well as providing an experimental validation of the geometric and kinematic properties.

Inverse Static Analysis of a Planar System With Spiral Springs

In this article the inverse static analysis of a two degrees of freedom planar mechanism equipped with spiral springs is presented. Such analysis aims to detect the entire set of equilibrium configurations of the mechanism once the external load is assigned. While on the one hand the presence of flexural pivots represents a novelty, on the other it extremely complicates the problem, since it brings the two state variables in the solving equations to appear as arguments of both trigonometric and linear functions. The proposed procedure eliminates one variable and leads to write two equations in one unknown only. The union of the root sets of such equations constitutes the global set of solutions of the problem. Particular attention has been reserved to the analysis of the “reliability” of the final equations: it has been sought the existence of critical situations, in which the solving equations hide solutions or yield false ones. A numerical example is provided. Also, in Appendix it is shown a particular design of the mechanism that offers computational advantages.