A Simple and Accurate Method for Determining Large Deflections in Complaint Mechanisms Subjected to End Forces and Moments

Compliant members in flexible link mechanisms undergo large deflections when subjected to external loads for which, traditional methods of deflection analysis do not apply Nonlinearities introduced by these large deflections make the system comprising such members difficult to solve Parametric deflection approximations are then deemed helpful in the analysis and synthesis of compliant mechanisms This is accomplished by seeking the pseudo-rigid-body model representation of the compliant mechanism A wealth of analysis and synthesis techniques available for rigid-body mechanisms thus become amenable to the design of compliant mechanisms In this paper, a pseudo-rigid-body model is developed and solved for the tip deflection of flexible beams for combined end loads with positive end moments A numerical integration technique using quadrature formulae has been employed to solve the nonlinear Bernoulli-Euler beam equation for the tip deflection Implementation of this scheme is relatively simpler than the elliptic integral formulation and provides nearly accurate results Results of the numerical integration scheme are compared with the beam finite element analysis An example for the synthesis of a compliant mechanism using the proposed model is also presented.

Analysis of the DLR Planetary Roller Spindle Drive

The DLR Planetary Roller Spindle Drive (PRSD), a new linear actuator developed at the German Aerospace Center (DLR), transforms fast rotation of a drive into slow but powerful linear movement. To optimize dynamical behaviour and performance of modified PRSD design versions, modelling and calculation methods have been developed, taking into account the very special requirements of this new design. To analyze the operating characteristics and performance figures, the DLR Planetary Roller Spindle Drive was modelled as a multibody system (MBS). Special attention was directed on the description of the complex contact mechanics between the PRSD elements. Accompanying experiments ensured the accuracy of the modelling. Analysis of the MBS model of an existing PRSD in the time domain showed satisfying accordance with testbench measurements.

Optimal Configurations for Flexible Redundant Robot Manipulators

The significant effect of initial configurations of flexible redundant robot manipulators is analyzed in the paper. It is found that the endpoint vibrations of a flexible redundant manipulator are quite different while performing the same endpoint trajectory starting from different initial configurations. Thus an optimal initial configuration with lower vibrations is found based on analysis before the manipulator starts to move. Only small and acceptable vibrations can be stimulated if the flexible redundant manipulator starts to move from the optimal configuration. Lots of computer time can be saved compared with optimal joint planning method. The method can be used in real-time control.

Kinematic Fixturing With Respect to a Plane Using Contact Sensing

This paper presents a method for determining the location of geometric elements that compose the external features of referencing fixtures. Since in most applications parts that are handled in robotic work-cells are on a worktable or a floor, this paper focuses on fixture geometries that reside on a plane of known location. The location of the unknown geometric elements are found using contacts to the geometric elements and spatial constraints between the geometric elements. Geometric equations for contacts between lines, planes, points, spheres, and cylinders are derived. Spatial constraint equations are also derived. An algorithm is given for locating the geometric elements that form the fixture. The algorithm uses the contact equations and spatial constraint equations to locate the geometric elements. To illustrate the use of this algorithm, two examples are described in detail.

Compliant Pantographs via the Pseudo-Rigid-Body Model

This paper uses a familiar classical mechanism, the pantograph, to demonstrate the utility of the pseudo-rigid-body model in the design of compliant mechanisms to replace rigid-link mechanisms, and to illustrate the advantages and limitations of the resulting compliant mechanisms. To demonstrate the increase in design flexibility, three different compliant mechanism configurations were developed for a single corresponding rigid-link mechanism. The rigid-link pantograph consisted of six links and seven joints, while the corresponding compliant mechanisms had no more than two links and three joints (a reduction of at least four links and four joints). A fourth compliant pantograph, corresponding to a rhomboid pantograph, was also designed and tested. The test results showed that the pseudo-rigid-body model predictions were accurate over a large range, and the mechanisms had displacement characteristics of rigid-link mechanisms in that range. The limitations of the compliant mechanisms included reduced range compared to their rigid-link counterparts. Also, the force-deflection characteristics were predicted by the pseudo-rigid-body model, but they did not resemble those for a rigid-link pantograph because of the energy storage in the flexible segments.

A Parametrization Scheme for the Burmester Curves

The cubic representation of the Burmester curve in Cartesian coordinates has certain disadvantages when automated searches are carried out. A parametric representation of the curve would be ideal. A systematic search could then be carried out by tracking points in a continuous fashion along the curve. In addition, solution rectification methods could be applied to determine the feasible segments, and the search could be limited to those portions only. This paper presents an alternative scheme for parametrizing the Burmester curves, as opposed to the complex number approach used by Chase et al. It uses the graphical method as its basis. The final scheme is not single valued, as it involves a parameter value as well a sign variable, but otherwise fulfils the requirements for an automatic search. It is an improvement on the cubic representation as it is double valued, rather than triple valued. The basic theory associated with the parametrization and the issues arising out of it are developed.

Solving the Kinematics of Planar Mechanisms

This paper presents a general method for the analysis of planar mechanisms consisting of rigid links connected by rotational and/or translational joints. After describing the links as vectors in the complex plane, a simple recipe is outlined for formulating a set of polynomial equations which determine the locations of the links when the mechanism is assembled. It is then shown how to reduce this system of equations to a standard eigenvalue problem, or if preferred, a single resultant polynomial. Both input/output problems and tracing-curve equations are treated.

A Parallely Actuated Work Support Module for Reconfigurable Machining Systems

In order to respond quickly to changes in market demands and the resulting product design changes, machine tool manufacturers must reduce the machine tool design lead time and machine set-up time. Reconfigurable Machine Tools (RMTs), assembled from machine modules such as spindles, slides and worktables are designed to be easily reconfigured to accommodate new machining requirements. The essential characteristics of RMTs are modularity, flexibility, convertibility and cost effectiveness. The goal of Reconfigurable Machining Systems (RMSs), composed of RMTs and other types of machines, is to provide exactly the capacity and functionality, exactly when needed. The scope of RMSs design includes mechanical hardware, control systems, process planning and tooling. One of the key challenges in the mechanical design of reconfigurable machine tools is to achieve the desired machining accuracy in all intended machine configurations. To meet this challenge we propose (a) to distribute the total number of degrees of freedom between the work-support and the tool and (b) employ parallely-actuated mechanisms for stiffness and ease of reconfigurability. In this paper we present a novel parallely-actuated work-support module as a part of an RMT. Following a brief summary of a few parallel mechanisms used in machine tool applications, this paper presents a three-degree-of-freedom work-support module designed to meet the machining requirements of specific features on a family of automotive cylinder heads. Inverse kinematics, dynamic and finite element analysis are performed to verify the performance criteria such as workspace envelope and rigidity. A prototype of the proposed module is also presented.

Design and Analysis of a Camera and Sensor Positioning Mechanism for ARIES: An Autonomous Mobile Robot

ARIES (Autonomous Robotic Inspection Experimental System) is a program for the Department of Energy (DOE) that was charged with the mission of surveying and inspecting drums containing low-level radioactive waste stored in warehouses at DOE facilities. This paper reports on the final development of the ARIES project, and focuses on the mechanical design and analysis of three mechanisms that position a camera and sensor package that sits atop a Cybermotion K3A mobile robotic platform. The ARIES project was executed through a joint effort of three parties: University of South Carolina (USC), Clemson University, and Cybermotion, Inc., of Salem, Virginia. The goal of the project was to develop an autonomous mobile robot that positions a data acquisition package (DAP) which surveys drums containing hazardous materials in Department of Energy (DOE) warehouses. The unique mechanical design of the positioning system is comprised of three distinct components: a lift mechanism, a fourbar mechanism, and a camera panning mechanism. The components are integrated in a manner that allows the DAP to be positioned from 0 to 16 feet off the ground while the robot maneuvers through aisles of drums in a warehouse. The three mechanisms, and the integration thereof, are reported in this paper.

Polynomial Solutions to the Displacement Analysis of 10-Link 1-DOF Mechanisms

This paper presents closed-form polynomial solutions to the displacement analysis problem of planar 10-link mechanisms with 1 degree-of-freedom (DOF). Using the successive elimination procedure presented herein, the input-output (I/O) polynomials as well as the number of assembly configurations for five mechanisms resulting from two 10-link kinematic chains are presented. It is shown that the displacement analysis problems for all five mechanisms can be reduced to a univariate polynomial devoid of any extraneous roots. This univariate polynomial corresponds to the I/O polynomial of the mechanism. In addition, one of the examples also illustrates how trigonometric manipulations in conjunction with tangent half-angle substitutions can lead to non-trivial extraneous roots in the solution process. Theoretical conditions for identifying and eliminating these extraneous roots are also presented.