Oren Masory

On the accuracy of a Stewart platform. I. The effect of manufacturing tolerances

Manufacturing tolerances, installation errors and link offsets cause deviations with respect to the nominal kinematic parameters of the platform. As a result, if the nominal values of these parameters are used within the platform control software, the resulting pose of the platform will be inaccurate. In order to evaluate the effects of the above factors on the platform accuracy, the inverse and forward kinematic problems of the actual platform model need to be solved. The authors present a numerical method for the solution of both problems and demonstrate, through simulation, the effect of the above factors on platform accuracy. The simulation results provide insight to the expected accuracy and indicate the major factors contributing to inaccuracies.<<ETX>>

Workspace evaluation of Stewart platforms

The workspace and the dexterity of a Stewart platform are affected by the choice of its major dimensions, actuator stroke and the kinematic constraints of its joints. An investigation of the effects of these parameters on workspace volume of the platform is presented. The obtained results were normalized so that they could be used as a design tool for the selection of dimensions, joints and actuators.

On the accuracy of a Stewart platform. II. Kinematic calibration and compensation

An effective algorithm for the identification of the kinematic parameters of a Stewart platform is presented and verified through simulations. The algorithm can be applied to both the reduced and the full models, which differ by the number of parameters to be identified. Compensation procedures for models are also presented. The algorithm was tested using simulated measurements that included realistic measurement noise, and the results showed that the platform pose error was reduced by at least one order of magnitude. The identification algorithm is computationally expensive and has to be performed on a powerful computer for practical implementation.<<ETX>>

Kinematic modeling and calibration of a Stewart platform

Manufacturing tolerances, installation errors and link offsets contaminate kinematic parameters of a nominal platform kinematic model. Since the platform controller determines the length of the leg actuators according to the nominal model, the resulting pose of the platform is inaccurate. To enhance the positioning accuracy of the platform, there is a need to estimate the actual values of these parameters and to incorporate these estimates into the inverse kinematic procedure performed by the machine controller. The objective of this paper is 2-fold. First, a new kinematic model is proposed to represent the errors due to imperfection of the U-joints and the ball-joints, which are key components of the Stewart platform. This model may be used to assist the design of the Stewart platform as the effects of mechanical tolerances of different components on the system accuracy can be fully explored. Secondly, an error-model-based method is devised for Stewart platform calibration, by which the accuracy of the Stewart platform can be greatly improved.

Evaluating the Uncertainty in Various Measurement Tasks Common to Accident Reconstruction

When performing calculations pertaining to the analysis of motor vehicle accidents, this paper describes how investigators must often select appropriate values for a number of parameters. The uncertainty of the final answer is a function of the uncertainty of each parameter involved in the calculation. This paper presents the results of recent tests that were conducted to obtain sample distributions of some common parameters, including measurements made with tapes, measurements made with roller-wheels, skidmark measurements, yawmark measurements, estimation of crush damage from photographs, and drag factors, that can be used to evaluate the uncertainty in an accident reconstruction analysis. The paper also reviews the distributions of some pertinent data reported by other researchers.

Autonomous Calibration of Hexapod Machine Tools

Hexapod machines are emerging as a new type of CNC machine tools, Among other things, stringent calibration is an important means to improve their accuracy, Traditionally, to perform system calibration, one needs to measure a number of machine poses using an external measuring device. However, this process is often labor-intensive and invasive, and difficult for on-line calibration. In this paper, a systematic way of self-calibrating a hexapod machine tool is introduced. By adding a small number of redundant internal sensors, errors of the hexapod machine tool can be measured. This approach has the potential of automatically producing high accuracy measurement data over the entire workspace of the system with an extremely fast measurement rate. Once the measurement data is available, a recursive filter is applied to estimate machine parameter errors from the predicted geometric errors, and to update the model residing in the machine controller. Thus, it is possible to dynamically calibrate and compensate for various types of machine errors including those induced by thermal and loading variations, without interrupting the normal operation of the machine tool. To verify the concept, preliminary experimental studies were conducted on a Stewart platform built at Florida Atlantic University.

Measurement of pose repeatabilty of stewart platform

Manufacturing tolerances, installation errors, link offsets, and controller errors effect the positioning repeatability of serial and parallel manipulators. A variety of measurement methods have been proposed and used to measure the repeatability of serial manipulators. However, these methods might not be suitable for parallel manipulators due to limited instrumentation accessibility and the large structure involved. This article describes two measurement procedures by which the position of a target point in three-dimensional space can be determined using a single theodolite that is used to collect two sets of measurements taken from two arbitrary locations. The required hardware needed for the implementation of this method is two standard measuring tapes installed vertically at two arbitrary locations, or one horizontal bar. If the target points are located on the end effector of a manipulator, its repeatability can be measured. The procedure that uses two vertical tapes was used to measure the repeatability of a Stewart Platform and experimental results are provided.

A simple method of accuracy enhancement for industrial manipulators

A robot calibration method which includes identification of kinematic parameters and error compensation is presented. The parameter identification process features an easy-to-perform measurement procedure using a low-cost, instrumented, articulated linkage, and with proper planning of the data collection process, the measurement of actual end effector positions can be performed automatically. The basis of the parameter identification approach is akin to that of closed-loop mechanism synthesis. For error compensation, a computation scheme based on the nominal model as opposed to the calibrated one is presented. The resulting algorithm, allowing the exploitation of the closed-form inverse kinematics solutions available for most industrial robots, is computationally efficient and therefore suited for on-line applications. Examples based on simulation studies, devised to include realistic operating conditions, are presented to demonstrate the feasibility of this method. The effects are also investigated of the number of measurements and of the sensor resolution on the overall quality of the identification.

Validation of the Circular Trajectory Assumption in Critical Speed

In a maneuver called a critical speed yaw, which occurs when a driver makes a dramatic steering input, the force required to turn the vehicle in the path requested exceeds the force that the tires are capable of generating. As a result, the vehicle turns in a path primarily defined by available friction and the vehicles velocity. Accident reconstructionists often use the critical speed model to determine vehicle speeds. This model assumes that the vehicles center of mass travels in a circular arc when in a critical speed yaw. This study investigates the validity of this assumption by comparing the results obtained by manually measuring the tire marks, assuming them parallel to the center of mass path, and fitting a polynomial. Findings indicate that the circular arc assumption is reasonably accurate. Results also indicate that 2nd order polynomial is a good approximation to describe the tire mark trajectory. The 3rd order polynomial might provide more accurate estimation for higher speed using the radius of curvature at x=0. Using the radius of curvature at midpoint of the trajectory provides results similar to the conventional method of measuring a chord and middle ordinate and calculating the radius.

Identification of Robot Kinematic Parameters Using Evolutionary Algorithms

ABSTRACTThis article proposes an alternative heuristic solution based on Genetic Algorithms (GAs) to the manipulator kinematic parameters identification problem. GAs, which refer to a family of algorithms that rely on analogies to natural evolution, have been applied to a wide range of optimization problems with extremely encouraging results. GAs outperform classical optimization techniques since they do not suffer from the disadvantages that are inherent to these methods. The formulation and the application of Genetic Algorithms for the solution of the above problem are discussed and the concept is verified by simulations in which the kinematic parameters of serial and parallel manipulators are identified. The results obtained demonstrate the simplicity and efficiency of this approach.