Proceedings of EuCoMeS, the first
Abstract: This paper addresses a class of 6-DOF parallel robots free of parallel singularities. This class is comprised of 3-legged robots that have spherical-prismatic pairs as their leg ends. The class notation is 3-XXSP where S and P stand for spherical and prismatic passive joints and X stands for any 1-DOF actuated joint. Following the reciprocal screws derivation, Grassmann-Cayley algebra is applied to find the singularity conditions of these robots. Then simple design guidelines are provided to avoid parallel singularities in the whole workspace.
D. Mundo, G. Fragomeni, G. Danieli, P. Fanghella, C. Balboni: A First Experimental Comparison between Non-Circular Gears Characterized by Teeth Designed According to Different Meshing Laws (received Nov 14 2005, final version Jan 24 2006)
Abstract: The paper shows a first experimental comparison between non circular gears having teeth designed according to two different methods: the constant angle of pressure method, and cycloidal profile method. In both cases, a pair of non-circular gears were generated, to drive a slider-crank mechanism designed to obtain a prescribed motion law. Such mechanism is designed to generate a pulsatile blood flow during cardiopulmonary bypass for cardiac surgery. The alternative motion consists of a quick forward stroke, corresponding to the Systolic phase, and a slow return stroke, corresponding to the diastolic phase.
Abstract: In the paper is presented a simulation system for parallel robots, which deals with the robot kinematics, workspace generation, singular position identification and trajectory visualization. The latest obtained results demonstrate that from the kinematic model and the graphical simulation the implemented algorithms offer a higher degree of generality. Therefore the developed simulation software modules may be applied to different types of parallel robots with three degrees of freedom. The computing time necessary for generating the virtual model is relatively small.
Abstract: Tendon-based Stewart platforms are capable of high speeds and accelerations. Thus, a reliable controller running with a high frequency is required. Here, an implementation based on a modular controller architecture is shown. To control the platform on a given trajectory, the implemented position control has to be extended by a tendon force control which generates defined and safe force values. In the case of one redundant tendon, a direct calculation is possible. Having at least two redundant tendons, the computation of a force distribution requires optimization methods, which are numerically expensive. In this paper, algorithms for both cases and their embedding into the controller are presented.
Abstract: Parameter determination and optimization play an important role for parallel kinematic machines since the machines properties depend significantly on an appropriate choice of the geometry. In this paper, the design of parallel machines is formulated in terms of a global constrained optimization problem, where the constraints are deduced from imperative process requirements e.g. size of the workspace and upper bounds on the kinematic dexterity. Furthermore, the total costs of the machine are proposed as objective function. It is shown, how this problem may be solved, applying interval analysis, and an implementation for parallel computation is introduced. Results for the parallel kinematic machine Linapod are presented.
Abstract: This paper presents an algorithm for detecting and computing the cusp points in the joint space of 3-RPR planar parallel manipulators. In manipulator kinematics, cusp points are special points, which appear on the singular curves of the manipulators. The nonsingular change of assembly mode of 3-RPR parallel manipulators was shown to be associated with the existence of cusp points. At each of these points, three direct kinematic solutions coincide. In the literature, a condition for the existence of three coincident direct kinematic solutions was established, but has never been exploited, because the algebra involved was too complicated to be solved. The algorithm presented in this paper solves this equation and detects all the cusp points in the joint space of these manipulators.
Abstract: For the determination of the kinematic dimensions of planar cam mechanisms certain graphical procedures like the hodograph method or the centrode method are available. A generalization of these methods does lead to graphical methods, which can also be used for the dimensioning of spherical and generally spatial cam mechanisms. The synthesis programme CADiS, which was developed at the Department of Mechanism Theory and Dynamics of Machines, does provide enhanced graphical methods within the user interface of a 3D-CAD-programme. Finally the synthesis of spatial cam mechanisms with the programme CADiS shall be demonstrated.
Abstract: This paper solves the identification of the geometric parameters of an end effector mounted probe with help of a sphere for a general spatial kinematic chain. The sphere with known radius can be placed generally in the workspace of the kinematic chain. Two possibilities of solving the nonlinear system of equations will be presented and evaluated on an example.
Abstract: We motivate and study the use of the forward kinematic model in the calibration scheme of parallel robots. Classical methods uses this model based only on the internal sensors for parameters elimination. One aim of the paper is to demonstrate how, in this well-constrained case, the model has numerous different solutions, how selecting a solution can lead to critical difficulties and possibly erroneous results. We propose two kind of alternatives, one drawing upon the methods of computer algebra to explicit the relation between the set of sensors and the parameters, and another which minimize the residual errors of an over-constrained formulation of the forward kinematics. This propositions are substantiated by experiments with planar robots, which are easy to describe completely and offer a full understanding of the underlying modeling and behavior.
P. Flores, J.C.P. Claro, J. Ambrósio, H.M. Lankarani: Computational Simulation of Mechanisms with Lubricated Revolute Joints: The Infinitely-Short Journal-Bearing Approach (received Nov 15 2005, final version Jan 10 2006)
Abstract: This paper deals with a methodology to assess the influence of the lubricated revolute joints in the kinematics and dynamics of mechanisms. The existence of the clearance at revolute joints is inevitable in all mechanical systems and most of them are designed to operate with a lubricant fluid. The infinitely-short journal-bearing approach for dynamic loads is used to evaluate the resulting hydrodynamic forces of the pressure distribution in the lubricated revolute joints. These hydrodynamic forces are then introduced into the system's equations of motion. A numerical example is presented in order to demonstrate the efficiency and accuracy of the methodology and procedures adopted.
Abstract: In this paper there are presented some considerations regarding ball-bearings' rings construction, assembling conditions, loading capacities, new constructions of ball-bearings having other number of balls or other dimensions of them in the way to have improved loading capacities. There are also presented theoretical and experimental researches in the field of loading capacities determination and researches on materials used in ball-bearings rings construction. Is presented an installation used in experimental researches for studies on rings having thick dimensions.
Abstract: This work deals with the theory of designing planar linkages and describes a new method of optimal dimensional deviations determination. The method allows to define the dimensional deviations directly for elements of planar linkage. In contrast to the matrix method pre-proposed by the authors the new one ensures definition of the global field of required deviations, including tolerances. The possibility of random assignment of the error function existence field is the specific feature of the suggested method. The developed method to calculate the length deviations for the multilink mechanisms links was used. For the method illustration, some examples of four-bar linkage and slider-crank mechanism positioning are presented. The results of the suggested and earlier stated methods are also compared.
Abstract: An attempt is made to present, with some semblance of unity, various representations and notions of rigid body displacement. Topics touched on include • equivalence between Euler parameters and real quaternions; homogeneity and norm, inversion and populating a homogeneous rotation matrix by rote, • dual quaternions, the Study condition and multiplication, • point, plane, octonian and subgroup transformation, • comparing planar mapping conventions and • an appendix containing a Grassmannian demonstration of transformative dual-adjoint equivalence and some simple examples using the general 8×8 transformation, its adjoint to compute “reciprocals” and its inverse. It is believed that these are revealed for the first time.
Abstract: In this paper the unconstrained motion (Error workspace) of some planar systems with joint clearance is analyzed. For the analysis, the joints are assumed to be revolute or translational. We also assume that all joint clearances are known. The kinematic image space is used to provide a geometric environment for the analysis of Error workspace. In this paper the Error workspace of a four-bar linkage, of a slider- crank mechanism and of two multiple-loop mechanisms are studied. Furthermore, mechanisms which have folding positions due to joint clearance are studied, too.
Abstract: The paper presents fully-isotropic redundantly-actuated parallel manipulators (RaPMs) with five degrees of freedom T3R2-type. The mobile platform has three independent translations (T3) and two rotations (R2). A method is proposed for structural synthesis of fully-isotropic T3R2-type RaPMs based on the theory of linear transformations. A one-to-one correspondence exists between the actuated joint velocity space and the external velocity space of the moving platform. The Jacobian matrix mapping the two vector spaces of fully-isotropic T3R2-type RaPMs presented in this paper is the identity 5×5 matrix throughout the entire workspace. The condition number and the determinant of the Jacobian matrix being equal to one, the manipulator performs very well with regard to force and motion transmission capabilities. Redundant actuation is used to obtain fully-isotropic T3R2-type parallel manipulators with elementary legs. As far as we are aware, this paper presents for the first time in the literature the use of redundancy to design fully-isotropic parallel manipulators as well as solutions of fullyisotropic RaPMs with five degrees of freedom.
Abstract: Traditional methods of cam profiling are based on determination of cam dimensions on the basis of allowable pressure angle without taking into account load conditions and without subsequent contact stress check. In this paper a procedure for determination of dimensions of a cam with a roller follower, which considers not only it's metric characteristics (displacement, analogues of velocity and acceleration), but also it's load conditions, is suggested.
O.J. Lara, C. Castejón, E. Laniado, H. Rubio, J.C. García-Prada: Kinematic Error Analysis in Harmonic Drive Transmissions using Lagrange's Equations and State Variables (received Oct 15 2005, final version Jan 13 2006)
Abstract: Harmonic Drive transmissions are widely used in modern design applications such as robotics, the aerospace and military industry, medical equipment or printing presses, because of advantages such as positional accuracy, high torque capabilities, low weight and volume, near zero backlash, versatility and high efficiency. Nevertheless, like all mechanical devices, they have disadvantages, such as the kinematic error, a little known parameter, which produces system resonances and basically depends on friction, compliance and assembly imperfections. In order to integrate an Harmonic Drive in a robotic system, it is necessary to know the kinematic error during rotation; this article deals with a mathematical model about the Harmonic Drive dynamical behavior, based on Lagrange formalism, and a novel representation by means of state variables of a lineal system in SIMULINK®, obtaining an acceptable simulation of Harmonic Drive kinematic error and its integration into an electromechanical system.
Abstract: The paper presents a mechanism able to reproduce the volumetric behaviour of a human ventricle in physiological conditions, based on the use of a pair of non-circular gears. The driven gear drives a three degrees of freedom (DOF) linkage.
Abstract: This paper presents the thorough investigation of four-link spatial RCCC mechanism (R, C are revolute and cylindrical pairs), including: new (fast and robust) algorithm for displacement analysis of the mechanism at the given input angle φ; dead positions of the mechanism (for regular cases and particular cases); four areas of values for constant mechanism parameters and corresponding subsets of RCCC mechanisms (input-crank, input-rocker, boundary and non-existent); domains of existence (over the input angle φ) for different cases of input-rocker and boundary mechanisms; all possible assembly modes for input-crank, input-rocker and boundary RCCC mechanism (cases with two and four assembly modes); the technique of formation of continuous position functions of links for each assembly modes in the corresponding domain of existence.
Abstract: The opto-electronic telecom market was the starting point for absolutely new technologies for many-axis alignment – often more than 12 axes. Nanotechnology requires still more resolution and accuracy. Improvement in accuracy can be achieved with adaptronic design principals and integration of piezo technology in the system design. The design rules for extreme high accurate multi axis systems lead to parallel structures. For high linear accuracy and large travel range are developed two new concepts, one use piezo actuator based walking drive mechanism and one use the mechatronic combination of piezo and motorized drives in one incremental sensor loop.  The first principle can be used in systems, where high stiffness, compactness but low speed is necessary, the second principle is just unlimited in speed and load, but needs new controller technology. Such a combined positioning system can satisfy the requirements of most experiments that require long-range motion and nanometer precision.
Abstract: This paper presents two new finite elements and its application in solving some problems in linear kinematic analysis of mechanisms. These elements highly increase the simplicity of the finite element method when applied in the resolution of velocity, acceleration, jerking and further derivatives. Likewise, it could also be used to solve some meshing situations in structural problems. These elements have also been used to solve position problems. The first element is defined to modelize point restraint on a line required to modelize prismatic joints in mechanisms. The other is useful whenever an angular restraint is to be considered. This article explains the mathematical developments leading to the matrices and vectors required to solve linear problems, while demonstrates their efficiency through some solved examples.
Abstract: Singular postures of 6R robots must be avoided because close to singularities an exact tracking of the planned end-effector trajectory requires great angular velocities in the rotary joints. Hence there is an interest in having a distance measure of the instantaneous configuration to the nearest singularity. This article outlines three new methods to measure the closeness to such a singularity. The presented measures are invariant with regard to Euclidean motions and similarities, they have a geometric meaning, and they can be computed in real-time.
Abstract: A mathematical formalization of so-called Assur's structural groups is given. It is based on the geometric theory of hinged devices. A criterion for a graph with vertices of two kinds (corresponding to free and fastened hinges) to be a structural scheme of an Assur's group in the plain is established.
Abstract: The subject of this paper is a diagram due to Martin Disteli. The diagram, illustrating the relation between the angular velocities of a pair of skew gears, is intended for the analysis of the relative screw motion between the two gears. The diagram, based on a circle, seems to have been overlooked by the community of kinematicians.
Abstract: The parallel robots dynamics requires a great deal of computing as regards the formulation of the generally nonlinear equations of motion and their solution. In this paper different solutions for solving the dynamical model for the guided in three points parallel robots are presented. The derived dynamical algorithms offer the possibility of a complex dynamic study for these parallel robots in order to evaluate their dynamic capabilities and to generate the control algorithms.
Abstract: In this paper a new measuring system is presented for determining the position and orientation of moving objects. It is composed by a wire-based measuring system CaTraSys (Cassino Tracking System) together with an inclinometer. The Kinematics and mechanical design of the system are presented. A prototype has been designed and built at LARM: Laboratory of Robotics and Mechatronics in Cassino. Experimental results are shown to validate and characterize the measurement system.
Abstract: The investigated five-leg robot with an axial spindle as platform (Pentapod Robot) is a parallel manipulator with five degrees of freedom. Up to solutions of a 32768-degree algebraic equation the direct kinematic problem could be solved as well as a geometric description of the singular positions of the robot spindle is given. The article describes the present state of our research.
Abstract: This paper describes a simple approach for avoiding first and second order singularities of the Frenet frame parameterization when moving along spatial curves with points of inflection or straight-line segments. To this end, a blending technique is introduced that uses C∞ transitions from regular segments to regularized normal vector calculations at inflection points and boundary points of linear segments using limit analysis based on de l'Hospital rule. As an example, the application of such trajectories to physical motion simulation with a serial robot is shown.
Abstract: In this paper we describe the Study quadric as the kinematic space for the group of all space congruences. We also demonstrate some of its properties from the point of view of modern differential geometry.
Abstract: The paper presents the procedure for the design of slider-crank mechanism when the stroke of the slider and the corresponding range of crank motion are given. It also discusses in details admissible input data for the mechanism. The method allows to select a mechanism from the family which is generated by using the angle of the crank position for the dead-position as the varying parameter. The procedure is simple and easily programmable.
Abstract: Sewing of fibre-reinforced composites (FRC) for complex three-dimensional structures as so called preforms is increasingly gaining in importance, both in the field of aerospace applications and in the field of automotive industry. In this paper, we first present a systematic procedure for the synthesis of a new mechanism for needle guidance in a sewing machine with single-side sewing technique. Then, we elaborate the kinematic model of the resulting mechanism. Finally, we present prototypes of the new needle guiding mechanism as well as the new single-side sewing machine and we exhibit first results from the mechanism test bench.
Abstract: In recent years more and more thermoplastic composites have been used in the development of new products. Besides the many other advantages the design flexibility makes it possible that the reinforced composites can be molded to reproduce almost any desired shape, especially in the form of space structure. In process of manufacture fibreglass reinforced products can be produced by compression molding in which a “matched mould” is needed. In this paper folding mechanisms are used as shape-orientated moulds which subject high pressure under high temperature and give product the required geometry in the consolidation process. The research on folding mechanisms includes structure synthesis and dimension synthesis, which specifically focus on how to divide required contour for finding a suitable mechanism by using contour symmetry and geometrical similar transformation. An example is given here, which shows the way like a folding mechanism as deployable structure can be used to unfold and stabilize spacer fabrics and spacer preforms for a given contour, namely sandwich structure, in the manufacture process.
Abstract: In this paper, we consider the problem of designing mechanical constraints for a planar serial chain formed with three revolute joints, denoted as the 3R chain. Our focus is on the various ways that two RR chains can be used to constrain the links of the 3R chain such that the system has one degree-of-freedom, yet passes through a set of five specified task positions.
Abstract: The kinematics of the gear hobbing process have been developed in order to predict and measure the cutting forces in the gear hobbing process. A review of past research in this area has highlighted the need to adopt a different approach to modelling the kinematics of the process in order to predict the cutting forces. The hobbing process has been described using six different co-ordinate systems and the kinematic relationships between these systems established. A single rack profile has been used to represent the profile of a single cutting tooth from the hob which was then extended to simulate the hob itself. The paper presents a summary of the development of the kinematic model and the instantaneous tooth space profile on the gear blank, as it is generated.
Abstract: The warm-up and cool-down behaviour of a KUKA KR-15/2 six-axis industrial robot for a particular task is measured and its effect on the robot repeatability determined. The robot is taught two poses. In each pose a tool-flange mounted laser points directly onto the CCD chip of a digital camera. The motion sequence is repeated for 15 hours (900 minutes) three different times at 30%, 75% and 10% of maximum robot speed. The temperature distribution history of the robot during the motion sequence is recorded with a thermal imaging camera. Temperatureinduced robot dimension changes are estimated from the geometry of the camera positions and how the laser spot migrates across the CCD chip over time from start to end. The results from the 30% run are used to estimate linear coefficients of thermal expansion. These empirical estimates are in the same order of magnitude as the coefficient corresponding to the aluminium alloy that is the dominant material comprising the robot links. The empirical coefficient of thermal expansion from the 30% run is used to predict the measured deformations for the 75% and 10% runs.
Abstract: In this paper, it is recalled that computer vision, used as an exteroceptive redundant metrology mean, simplifies the control of a Gough-Stewart parallel robot. Indeed, contrary to the usual methodology where the robot is modeled independently from the control law which will be implemented, we take, since the early modeling stage, into account that vision will be used for control. Hence, kinematic modeling and projective geometry are fused into a control-devoted vision-based kinematic model through the observation of its legs. Thus, this novel vision-based kinem atic modeling is extended to two other parallel manipulator families, namely Orthoglide and I4L. Inspired by the geometry of lines, this kind of model unifies and simplifies both identification and control. Indeed, it has a reduced parameter set and yields a linear solution to calibration. Using the same models, visual servoing schemes are presented, where the directions of the non-rigidly linked legs are servoed, rather than the end-effector pose.
Abstract: In this paper a workspace analysis has been presented for serial RRP manipulators. The cross-section boundary curve of this kind of manipulators can be described by a 8-th order polynomial of radial and axial reaches in Cartesian Space. Special cases are studied in order to illustrate different designs of RRP manipulators and the effect of some design parameters on the position workspace. An analysis of an industrial RRP manipulator is presented as a case of study.
Last update: Aug 27, 2009 by H.-P. Schröcker.