An algorithm for the forward kinematics of general 6 dof parallel manipulators (original) (raw)
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The Forward Kinematics Problem with an exact algebraic Method for the general parallel robot
This article introduces an exact method to solve the forward kinematics problem (FKP) specifically applied to spatial parallel manipulators. The majority can modeled by the 6-6 parallel manipulator. This manipulator is a hexapod made up of a fixed base and a mobile platform attached to six kinematics chains with linear (prismatic) actuators located between two ball or Cardan joints. In order to implement algebraic methods, the parallel manipulator kinematics will be formulated as polynomial equations systems where the equation number is equal to the unknown numbers. One position-based kinematics model will be identified to solve the difficult FKP. The selected proven algebraic method implements Gröbner bases and constructs an equivalent univariate polynomial system. The exact resolution of this last system determines the real solution which exactly corresponds to the manipulator postures. The FKP resolution of the general 6-6 parallel manipulator outputs 40 complex solutions. We provide several examples of various hexapod types yielding eight real solutions. This algebraic method is exact and computes certified results.
Advanced Robotics, 2005
This article introduces an exact method to solve the forward kinematics problem (FKP) specifically applied to spatial parallel manipulators. The majority can modeled by the 6-6 parallel manipulator. This manipulator is a hexapod made up of a fixed base and a mobile platform attached to six kinematics chains with linear (prismatic) actuators located between two ball or Cardan joints. In order to implement algebraic methods, the parallel manipulator kinematics will be formulated as polynomial equations systems where the equation number is equal to the unknown numbers. One position-based kinematics model will be identified to solve the difficult FKP. The selected proven algebraic method implements Gröbner bases and constructs an equivalent univariate polynomial system. The exact resolution of this last system determines the real solution which exactly corresponds to the manipulator postures. The FKP resolution of the general 6-6 parallel manipulator outputs 40 complex solutions. We provide several examples of various hexapod types yielding eight real solutions. This algebraic method is exact and computes certified results.
Direct kinematics of planar parallel manipulators
1996
Abstract We address the problem of finding all the solutions of the direct kinematics for every possible architectures of planar fully parallel manipulators. We show that for this problem all the possible kinematic chains can be reduced to a set of three basic chains and we explain how to calculate the solutions of the forward kinematics for all the combinations of these basic chains and consequently for all the possible architectures of planar parallel robots
The Kinematics and the Full Minimal Dynamic Model of a 6DOF Parallel Robot Manipulator
Nonlinear Dynamics, 1999
In this paper we present a particular architecture of parallel robots which has six-degrees-of-freedom (6-DOF) with only three limbs. The particular properties of the geometric and kinematic models with respect to that of a classical parallel robot are presented. We show that inverse problems have an analytical solution. However, to solve the direct problems, an efficient numerical procedure which needs
A General Geometric Index for Solving the Forward Kinematics of Planar Parallel Manipulators
2021 9th RSI International Conference on Robotics and Mechatronics (ICRoM), 2021
In this paper, a new geometrical method is proposed to solve the forward kinematics of planar parallel manipulators exhibiting two translational and one rotational DOF which leads to high-order system polynomial expressions. The main idea has arisen from a geometrical interpretation of the intersection among the vertex space of each kinematic chain. From the type synthesis performed for planar parallel manipulators with identical kinematic structure, it has been revealed that the number of every possible configuration for this type of manipulators is eighteen, which the solution of the forward kinematic problem can be expressed using a univariate polynomial expression. However, among these eighteen configuration only six of them lead to high order polynomials and therefore do not have closedform solutions. The proposed method in this paper is based on an index representing the intersection of the circles which are extracted from the vertex space of each kinematic limb of the manipulator. In this approach, the orientation angle of the moving platform is selected from an interval; and based on the selected orientation angle, the circles obtained from the vertex space of each limb are determined. The forward kinematic solution happens where all the circles intersect at one common point where this geometrical phenomenon is expressed using the proposed index. In order to illustrate the performance of the proposed approach, three examples are solved. It should be noted that the foregoing method succeeded even in solving examples such as manipulators with six real solutions, manipulators with degenerate answers, which are reported in the literature as special cases.
Methods to solve forward kinematics of parallel and serial manipulators
AIP Conference Proceedings
In this paper, approaches for the solution of parallel manipulators forward kinematics have been addressed. Current research on this topic has been analyzed to determine the status and unresolved issues of the research field. Articles on parallel manipulators forward kinematics were reviewed, and numerous approaches for resolving forward kinematics in particular have been identified and published, which may assist researchers in selecting the most appropriate technique for solving the problem in this domain. Researchers have also attempted to apply these methods to a variety of other parallel manipulator-related problems, such as inverse kinematics and dynamics. In robotics, serial manipulators were invented before parallel manipulators. Hence, methodologies for solving forward kinematics were first developed for serial manipulators and many methods are ineffective for parallel manipulators. In this paper, all identified methods can be used for solving forward kinematics of parallel and serial manipulators.
The direct kinematics of planar parallel manipulators: Special architectures and number of solutions
Mechanism and Machine Theory, 1994
We address the problem of finding all the solutions of the direct kinematics for every possible architectures of planar fully parallel manipulators. We show that for this problem all the possible kinematic chains can be reduced to a set of three basic chains and we explain how to calculate the solutions of the forward kinematics for all the combinations of these basic chains and consequently for all the possible architectures of planar parallel robots.
2005
Based on a proven exact method to solve the forward kinematics problem , this article is the second one investigating the forward kinematics problem formulation specifically applied to planar parallel manipulators. This part focuses on the displacement based equation systems. The majority of planar tripods can modeled by the 3-RPR parallel manipulator which is a tripod constituted by a fixed base and a triangular mobile platform attached to three kinematics chains with linear (prismatic) actuators located between two revolute joints. In order to implement the algebraic method, the parallel manipulator kinematics shall be formulated as polynomial equation systems where the number of equations are equal or exceeding the unknown numbers. Three geometric formulation were derived to model the difficult forward kinematics problem . The selected algebraic proven method is implementing Gröbner bases from which it constructs an equivalent univariate system. Then, the real roots isolation is performed using this last system. Each real solution exactly corresponds to one manipulator assembly mode. The forward kinematics problem resolution of the planar 3-RPR parallel manipulator outputs 6 complex solutions which become a proven real solution number upper bound. In several typical examples, the resolution performances (computation times and memory usage) are compared. It was then possible to compare the modelings and to reject one. Moreover, the number of real solutions was obtained and the corresponding postures drawn. The algebraic method is exact and produces certified results.
On the Kinematic Analysis of a Spatial Six-Degree-of-Freedom Parallel Manipulator
Scientia Iranica
In this paper, a novel spatial six-degree-of freedom parallel manipulator actuated by three base-mounted partial spherical actuators is studied. This new parallel manipulator consists of a base platform and a moving platform, which are connected by three legs. Each leg of the manipulator is composed of a spherical joint, prismatic joint and universal joint. The base-mounted partial spherical actuators can only specify the direction of their corresponding legs. In other words, the spin of each leg is a passive degree-of-freedom. The inverse pose and forward pose of the new mechanism are described. In the inverse pose kinematics, active joint variables are calculated with no need for evaluation of the passive joint variables. To solve the forward pose problem, a much simpler method compared to the traditional method is introduced. Closed form relations for the inverse and forward rate kinematics are proposed. Finally, two sets of singular connguration of the newly introduced manipulat...