Showing papers on "Kinematics equations published in 1997"
TL;DR: In this paper, the kinematics and dynamics of a six-degree-of-freedom platform-type parallel manipulator with six revolute legs are presented, where each leg consists of two links that are connected by a revolute joint.
Abstract: This paper presents the kinematics and dynamics of a six-degree-of-freedom platform-type parallel manipulator with six revolute legs, i.e. each leg consists of two links that are connected by a revolute joint. Moreover, each leg is connected, in turn, to the base and moving platforms by means of universal and spherical joints, respectively. We first introduce a kinematic model for the manipulator under study. Then, this model is used to derive the kinematics relations of the manipulator at the displacement, velocity and acceleration levels. Based on the proposed model, we develop the dynamics equations of the manipulator using the method of the natural orthogonal complement. The implementation of the model is illustrated by computer simulation and numerical results are presented for a sample trajectory in the Cartesian space.
61 citations
TL;DR: A new technique for deriving dynamic equations of motion for serial chain and tree topology mech anisms with common nonholonomic constraints by automatically producing a minimum set of equations ofmotion that do not include La grange multipliers.
Abstract: This article describes a new technique for deriving dynamic equations of motion for serial chain and tree topology mech anisms with common nonholonomic constraints. For each type of nonholonomic constraint, the Boltzmann-Hamel equations produce a concise set of dynamic equations. These equations are similar to Lagrange's equations and can be applied to mechanisms that incorporate that type of constraint. A small library of these equations can be used to efficiently analyze many different types of mechanisms.Nonholonomic constraints are usually included in a La grangian setting by adding Lagrange multipliers and then eliminating them from the final set of equations. The ap proach described in this article automatically produces a minimum set of equations of motion that do not include La grange multipliers.
45 citations
20 Apr 1997
TL;DR: This work proposes a new approach to solving the point-to-point inverse kinematics problem for highly redundant manipulators that explicitly takes into account constraints due to joint limits and self-collisions and central to this approach is the novel notion of kinematic roadmap for a manipulator.
Abstract: We propose a new approach to solving the point-to-point inverse kinematics problem for highly redundant manipulators. It is inspired by recent motion planning research and explicitly takes into account constraints due to joint limits and self-collisions. Central to our approach is the novel notion of kinematic roadmap for a manipulator. The kinematic roadmap captures the connectivity of the configuration space of a manipulator in a finite graph like structure. The standard formulation of inverse kinematics problem is then solved using this roadmap. Our current implementation, based on Ariadne's clew algorithm, is composed of two sub-algorithms: EXPLORE, a simple algorithm that builds the kinematic roadmap by placing landmarks in the configuration space; and SEARCH, a local planner that uses this roadmap to reach the desired end-effector configuration. Our implementation of SEARCH is an extremely efficient closed form solution, albeit local, to inverse kinematics that exploits the serial kinematic structure of serial manipulator arms. Initial experiments with a 7-DOF manipulator have been extremely successful.
27 citations
20 Apr 1997
TL;DR: This paper presents analytical solutions for the forward displacement and velocity kinematics of the "321-HEXA", a fully-parallel manipulator design with R-RR-RRR legs as in the " HEXA" design and with a "3-2-1" top platform.
Abstract: This paper presents analytical solutions for the forward displacement and velocity kinematics of the "321-HEXA", a fully-parallel manipulator design with R-RR-RRR legs as in the "HEXA" design and with a "3-2-1" top platform. The forward position and velocity kinematics rely on simple geometric algorithms that find the position and velocity of the top of a tetrahedron from the knowledge of the tetrahedron's side lengths as well as the position and velocity of the base triangle points. The forward position kinematics give eight solutions, requiring linear and quadratic equations only. The inverse kinematics requires the solution of one quartic equation for each leg.
25 citations
TL;DR: A new model of parallel manipulator for manufacturing, whose mechanism comes from the general Stewart platform which has the advantages of high rigidity and high load capacity is presented.
20 citations
20 Apr 1997
TL;DR: An algebraic analysis of the closure equation obtained for arbitrary single loop spatial kinematic chains is presented, which allows us to design an efficient interval method for solving their inverse kinematics.
Abstract: We present an algebraic analysis of the closure equation obtained for arbitrary single loop spatial kinematic chains, which allows us to design an efficient interval method for solving their inverse kinematics. The solution of a kinematic equation can be factored into a solution of both its rotational and its translational components. We have obtained general and simple expressions for these equations and their derivatives that are used to perform Newton cuts. A branch and prune strategy is used to get a set of boxes as small as desired containing the solutions. If the kinematic chain is redundant, this approach can also provide a discretized version of the solution set. The mathematics of the proposed approach are quite simple and much more intuitive than continuation or elimination methods. Yet it seems to open a promising field far further developments.
18 citations
20 Apr 1997
TL;DR: The proposed statistical approach to the Fourier modelling gives clear guidelines towards the optimisation of the robot kinematics and points out structural characteristics of the trajectory planning algorithms.
Abstract: A new approach to the analysis and design of robot manipulators is presented. The novel feature resides on a non-standard formulation to the modelling problem. Usually, system descriptions are based on a set of differential equations which, in general, require laborious computations and may be difficult to analyse. These facts motivate the need of alternative models based on different mathematical concepts. The proposed statistical approach to the Fourier modelling gives clear guidelines towards the optimisation of the robot kinematics and points out structural characteristics of the trajectory planning algorithms.
13 citations
07 Jul 1997
TL;DR: This paper addresses the kinematics modeling of a four legged mobile robot which has been developed to study the leg swinging and robot motion during locomotion and presents a closed kinematic chain algorithms of the whole robot structure.
Abstract: This paper addresses the kinematics modeling of a four legged mobile robot which has been developed to study the leg swinging and robot motion during locomotion. The robot motion is categorized into: The leg swinging motion as an open loop kinematics chain and the robot trunk motion relative to the feet during locomotion as a closed kinematics chain. Algorithms for solving the forward and inverse kinematics problems of these two categories have been developed. A closed kinematics chain algorithms of the whole robot structure is presented. This closed kinematics model is used in off-line animation of the robot motion in different cases and to simulate the stable wave gait in off-line programming. The robot motion by computer graphics is displayed.
13 citations
12 Oct 1997
TL;DR: In this article, the authors present a necessary and sufficient condition for a cable-suspended robot to achieve static equilibrium at a given configuration. This condition is based on the left null space of an augmented manipulator Jacobian and is easily implemented as an algorithm for testing configurations.
Abstract: The paper examines some issues concerning the inverse kinematics and statics of cable suspended robots and studies some of the inherent workspace limitations that result from the fact that the robot is cable actuated. The paper presents a necessary and sufficient condition for a cable suspended robot to be capable of achieving static equilibrium at a given configuration. This condition is based on the left null space of an augmented manipulator Jacobian and is easily implemented as an algorithm for testing configurations. To illustrate the efficacy of the results, planar and fully spatial examples are presented.
13 citations
20 Apr 1997
TL;DR: Techniques for automatically identifying and modeling the kinematic constraints of manipulated objects and joints with configuration and history dependent forces are proposed.
Abstract: This paper proposes techniques for automatically identifying and modeling the kinematic constraints of manipulated objects. The existence of constraints is established by examination of the forces and torques normal and tangential to the object's motion. Constraints are modeled as joints with configuration and history dependent forces. To illustrate these concepts, several experimental examples are presented.
9 citations
07 Jul 1997
TL;DR: In this paper, a new method for solving the inverse kinematics problem of elastic link manipulators is presented, which is considered as a differential algebraic problem with differential equations of motion and kinematic constraints to be satisfied.
Abstract: In this paper a new method for solving the inverse kinematics problem of elastic link manipulators is presented. The inverse kinematics problem is considered as a differential-algebraic problem with differential equations of motion and kinematic constraints to be satisfied. A method to integrate this system of equations by partitioning the generalized coordinates and using Newton-Raphson iterations at each integration step is proposed. The stability of the method is analyzed. To improve the overall trajectory tracking performance, use of vibration suppression control at the end of motion is suggested. Experimental results with a spatial flexible link manipulator demonstrate a reasonable performance.
07 Aug 1997
TL;DR: Important requirements for modeling electro-mechanical assemblies are identified, including positioning and orienting components, verifying kinematic joints, propagating mating constraints, and capturing joint attributes.
Abstract: Design of electro-mechanical products involves the description of the constraints between a group of parts that allows them to behave in the desired fashion. This includes the description of the relative motion between components, fit requirements, and joint strength requirements. While some of these constraints are generated during the conceptual design stage, additional details are developed during the preliminary and detailed design stages. Any such information generated during a previous level of the design needs to be captured and propagated to the next lower level of design. In this paper, we identify important requirements for modeling electro-mechanical assemblies. These are: positioning and orienting components, verifying kinematic joints, propagating mating constraints, and capturing joint attributes. To support these modeling activities, we present assembly representations to capture the joint kinematics information and component degrees of freedom generated during the detailed design stage.
07 Jul 1997
TL;DR: A technique is presented to measure the absolute position of a robot and any other strategic positions within the workcell, and also its specially built control software and PC based control software.
Abstract: In this study, a technique is presented to measure the absolute position of a robot and any other strategic positions within the workcell, and also its specially built control software. One of the most important factors affecting the absolute or world accuracy of robots is the variation in arm geometry from a perfect kinematics form. Since arm position is essentially controlled by means of joint angles, Cartesian co-ordinates of the tool centre point are derived from the forward kinematics transform equations assuming a perfect kinematics form. Any deviation from this perfect case will result in world positional errors and hence, for effective off-line programming it is important to calibrate the real robot hardware against the virtual model used by the robot simulation computer systems. This paper reports on work carried out in developing such a low cost calibration technique, its PC based control software and performance monitoring systems.
07 Jul 1997
TL;DR: The proposed statistical approach to the Fourier modelling gives clear guidelines towards the optimisation of the robot kinematics and point out structural characteristics of the trajectory planning algorithms.
Abstract: A new approach to the analysis and design of robot manipulators is presented. The novel feature resides on a non-standard formulation to the modelling problem. Usually, system descriptions are based on a set of differential equations which, in general, require laborious computations and may be difficult to analyse. These facts motivate the need of alternative models based on different mathematical concepts. The proposed statistical approach to the Fourier modelling gives clear guidelines towards the optimisation of the robot kinematics and point out structural characteristics of the trajectory planning algorithms.
20 Apr 1997
TL;DR: Analytical solutions for the forward displacement kinematics of the "31-12" fully parallel manipulator design, requiring nothing more difficult than the solution of quadratic equations.
Abstract: This paper presents analytical solutions for the forward displacement kinematics of the "31-12" fully parallel manipulator design. In this design, three points in the base platform are linked to one single point in the top platform, while two of the remaining top platform points are linked to a single point in the base. Neither the base nor the top platforms of the manipulator have to be planar. The forward position kinematics give eight solutions, requiring nothing more difficult than the solution of quadratic equations.
TL;DR: In this paper, the dot product of the bases vectors on the super-surface of the non-linear nonholonomic constraints with one order, expressed by quasi-coordinates, and Mishirskii equations are regarded as the fundamental equations of dynamics with nonlinear and non-holonomic constraint in one order for the system of the variable mass.
Abstract: The dot product of the bases vectors on the super-surface of the non-linear nonholonomic constraints with one order, expressed by quasi-coordinates, and Mishirskii equations are regarded as the fundamental equations of dynamics with non-linear and non-holonomic constraints in one order for the system of the variable mass. From these the variant differential-equations of dynamics expressed by quasi-coordinates are derived. The fundamental equations of dynamics are compatible with the principle of Jourdain. A case is cited.