The direct kinematics of planar parallel manipulators: Special architectures and number of solutions (original) (raw)

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

Direct Kinematics and Assembly Modes of Parallel Manipulators

The International Journal of Robotics Research, 1992

In this article we address the problem of the direct kinematics of parallel manipulators and the corollary problem of their assembly modes (i.e., the different ways of assembling these mechanisms when their geometry are fixed).

Unified Kinematic Analysis of General Planar Parallel Manipulators

Journal of Mechanical Design, 2004

A kinematic mapping of planar displacements is used to derive generalized constraint equations having the form of ruled quadric surfaces in the image space. The forward kinematic problem for all three-legged, three-degree-of-freedom planar parallel manipulators thus reduces to determining the points of intersection of three of these constraint surfaces, one corresponding to each leg. The inverse kinematic solutions, though trivial, are implicit in the formulation of the constraint surface equations. Herein the forward kinematic solutions of planar parallel robots with arbitrary, mixed leg architecture are exposed completely, and in a unified way, for the first time.

An algorithm for the forward kinematics of general 6 dof parallel manipulators

1990

Résumé: Forward kinematics has been studied mainly for parallel manipulators with planar faces. In this case the size of the set of equations from the inverse kinematics can be reduced from 6 to 3 and this last set can be combined into a polynomial in one variable of order 16. But this method cannot be extended to general parallel manipulators without planar faces for which there is no known results.

On the Direct Kinematics Problem of Parallel Mechanisms

Journal of Robotics

The direct kinematics problem of parallel mechanisms, that is, determining the pose of the manipulator platform from the linear actuators’ lengths, is, in general, uniquely not solvable. For this reason, instead of measuring the lengths of the linear actuators, we propose measuring their orientations and, in most cases, also the orientation of the manipulator platform. This allows the design of a low-cost sensor system for parallel mechanisms that completely renounces length measurements and provides a unique solution of their direct kinematics.

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.

Direct kinematics of parallel manipulators

IEEE Transactions on Robotics and Automation, 1993

ilv chosen. Desired velocities at certain points along the path are-. to be specified and can be 7ero. pohitive, or negative. Thercfore, stopping and reversing phases can be included by specifying the desired velocities accordingly. The convergence to the terminal cohfiguration is exponential. Simulation results showed that the desired path was followed and the desired velocities were achieved. Different velocity profiles can be chosen by changing the structure of the control law for the tangential velocity U. An extension to other types of path segments than arcs of circles to have smoother transitions between the path segments can be a topic for further research.

Singular configurations and direct kinematics of a new parallel manipulator

Proceedings 1992 IEEE International Conference on Robotics and Automation, 1992

We present in this paper a new mechanical architecture for a parallel manipulator. We address the problem of the determination of the singular configurations of this architecture. Then we show that the direct kinematic problem has at most 16 solutions and exhibit an algorithm to find all the solutions.

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.