Inverse Displacement Problem Research Articles

Inverse kinematics and singularity analysis of a redundant parallel robot

The 3C (computer, communications, consumer electronics) industry belongs to labor-intensive and the requirements of the 3C industry are precisely high. The parallel robot is a good choice to replace human labor to manufacture these products. This paper presents a new 3- redundant parallel mechanism for 3C manufacturing. Firstly, some advantages of redundant parallel robots in the current industrial demand are discussed. Then, the inverse kinematics of the redundant parallel manipulator is analyzed according to the closed-loop equation, the inverse displacement problem is solved. The machine is simple and low cost, and as a less freedom robot, it has a higher precision than the traditional robot and has a broad prospect for 3C manufacturing. Finally, the Jacobian matrix of the redundant parallel manipulator was calculated and established by the inverse kinematics formula, and three kinds of the singularity of the mechanism were analyzed by the Jacobian matrix, which are the forward singularity, reverse singularity, mixed singularity respectively.

Kinematics Analysis of 6-Degrees-of-Freedom Parallel + Serial Type Hybrid Mechanisms Containing Parallel Mechanism With High Coupling Motions

AbstractThe existing displacement of parallel + serial type hybrid mechanisms is mainly solved by the equivalent serial mechanism (SM) method. However, a large number of lower mobility parallel mechanisms (PMs) that have high coupled motions at the end-effector cannot be equivalent to SMs. Thus, the displacement problem especially for the inverse displacement of this type of hybrid mechanisms has not been well solved. On the basis of this situation, this article takes a 6-degrees-of-freedom (DOFs) 3-UPU + 3R hybrid mechanism as an example to give a general method to solve the displacement problem. First, based on the inverse displacement and pose coupling relationship of the 3-UPU PM, its forward displacement is solved by Sylvester’s dialytic elimination method, and then the forward displacement of the 3-UPU + 3R hybrid mechanism is obtained by the superposition method. Second, by skillfully dealing with the relationship between coupling motions of the 3-UPU PM and the motion of hybrid mechanism, three nonlinear equations containing three unknown motion parameters are obtained, and the inverse displacement problem is solved using Sylvester’s dialytic elimination. The research in this article is valuable in the kinematics modeling of hybrid mechanisms.

An iterative algorithm for inverse displacement analysis of Hyper-redundant elephant’s trunk robot

AbstractThis paper proposes an iterative algorithm to solve the inverse displacement for a hyper-redundant elephant’s trunk robot (HRETR). In this algorithm, each parallel module is regarded as a geometric line segment and point model. According to the forward approximation and inverse pose adjustment principles, the iteration process can be divided into forward and backward iteration. This iterative algorithm transforms the inverse displacement problem of the HRETR into the parallel module’s inverse displacement problem. Considering the mechanical joint constraints, multiple iterations are carried out to ensure that the robot satisfies the required position error. Simulation results show that the algorithm is effective in solving the inverse displacement problem of HRETR.

Inverse displacement analysis of a novel hybrid humanoid robotic arm

The application of hybrid mechanisms in the field of humanoid robots has attracted significant attention. A novel eight-degree-of-freedom hybrid manipulator is proposed to realize a kinematic function similar to that of the human arm. A general method for solving the inverse displacement problem of hybrid mechanisms is given, and the proposed humanoid robotic arm is taken as an example to demonstrate the solution process of this method. Furthermore, a closed-form solution for the inverse displacement problem of the hybrid humanoid robotic arm is derived by using the given method based on screw theory, exponential product formula, and Paden–Kahan subproblems. In addition, the problem of verifying and selecting the appropriate solutions according to the starting postures is also illustrated in a series of simulation experiments. Simulation experiment results show that there are (at most) 32 sets of solutions for the proposed humanoid robotic arm according to the same target position-orientation matrix and the given redundant input variables, and the accuracy of the proposed method for solving the inverse displacement problem is verified.

Inverse Displacement Analysis of a Hyper-redundant Elephant’s Trunk Robot

This paper deals with inverse displacement analysis of a Hyper-redundant Elephant’s Trunk Robot (HRETR). The HRETR is connected in series with n modules of 3UPS-PRU parallel mechanism where the underline P denotes an active prismatic joint. Based on the idea of differential geometry, backbone curve of the robot is formulated by using a parametric function consisting of sub-functions and control parameters. A general algorithm for generating a backbone curve and fitting the modules to the backbone curve is proposed. In this way, the inverse displacement analysis of the robot can be carried out by solving the inverse displacement problem of each parallel mechanism module and taking into account the length limits of the links. A HRETR with 6 modules is taken as an example to demonstrate the applicability of the algorithm.

On the use of the dual Euler–Rodrigues parameters in the numerical solution of the inverse-displacement problem

The Euler–Rodrigues parameters (ERP) are revisited in this paper, the motivation being the need for a systematic methodology to formulate the inverse-displacement problem associated with a six-revolute (6R) serial robot. Although significant progress was made in the solution of the problem in the eighties and nineties, there is not one algorithm adopted by the research and applications communities, but rather various algorithms that lead to the resolvent polynomial of 16th degree or lower. In this paper the problem is formulated using the dual ERP. Motivated by the lack of a methodology that would allow R&D professionals to readily implement a generic solution algorithm in industrial environments requiring real-time inverse-displacement problem (IDP) solutions. An inverse-displacement numerical solution of 6R robots of arbitrary architecture is proposed. This is the main thrust of the paper. The contribution of the paper is a systematic procedure to formulate the problem and implement its solution by numerical means. The procedure is illustrated with the example of an industrial robot whose architecture does not allow for a closed-form solution.

A univariate marginal distribution algorithm based on extreme elitism and its application to the robotic inverse displacement problem

In this paper, a univariate marginal distribution algorithm in continuous domain (UMDA C ) based on extreme elitism (EEUMDA C ) is proposed for solving the inverse displacement problem (IDP) of robotic manipulators. This algorithm highlights the effect of a few top best solutions to form a primary evolution direction and obtains a fast convergence rate. Then it is implemented to determine the IDP of a 4-degree-of-freedom (DOF) Barrett WAM robotic arm. After that, the algorithm is combined with differential evolution (EEUMDA C -DE) to solve the IDP of a 7-DOF Barrett WAM robotic arm. In addition, three other heuristic optimization algorithms (enhanced leader particle swarm optimization, intersect mutation differential evolution, and evolution strategies) are applied to find the IDP solution of the 7-DOF arm and their performance is compared with that of EEUMDA C -DE.

GEOMETRIC APPROACH TO SOLVING THE INVERSE DISPLACEMENT PROBLEM OF CALIBRATED DECOUPLED 6R SERIAL ROBOTS

This paper presents a simple but efficient way to numerically calculate the inverse displacement problem of calibrated decoupled 6R serial robots. The method is iterative and works with any type of calibrated robot model, such as level-3 models, since it requires no algebraic computation and no resolution of high-order polynomials, only the computation of the forward displacement problem of the calibrated robot model and the inverse kinematics of the nominal robot model. The method proposed can find up to eight possible solutions for a given end-effector pose. A numerical example is presented, with one million arbitrary end-effector poses of a level-3 calibrated ABB IRB 120 robot. The computation time for solving the inverse problem is analyzed, and in most cases is found to be only four times the time needed to calculate the nominal inverse kinematics and the calibrated direct kinematics. Furthermore, the method is fast enough to be implemented directly into the robot controller using the RAPID programming language.

Kinematics Analysis of a 3-RRR Spherical Parallel Mechanism with Coaxial Input Shafts

As an important mechanism with special and extensive application, the three degrees of freedom spherical parallel mechanism is always a research hot in the mechanical fields. In this paper, the feature of the 3-RRR spherical parallel mechanism with coaxial input shafts is introduced, and its motion feature is analyzed based on the screw theory. The mobility of the spherical parallel mechanism is calculated by using the Modified Kutzbach-Grübler criterion, and the inverse displacement problem of the mechanism is solved. Then the expression of the Jacobian matrix is deduced based on the kinematics equation and its inverse solution. The contents of this paper should be useful for the further application of the spherical parallel mechanism.

Workspace and stiffness analysis of a three-degree-of-freedom spatial cable-suspended parallel mechanism while considering cable mass

Most existing research on parallel cable-driven mechanisms has been performed while neglecting cable mass. However, those prior works that did take cable mass into account have shown that such a hypothesis may lead to significant errors in the analysis of these mechanisms. The research presented herein assesses the effect of neglecting cable mass in the analysis of a spatial parallel three-degree-of-freedom suspended cable-driven mechanism. The analysis is based on the elastic catenary model. The inverse displacement problem of the mechanism is solved numerically subject to constraints on the cable tensions and restrictions on cable drooping. This solution is then used in the numerical estimation of the mechanism workspace. The stiffness of the mechanism is evaluated throughout the workspace by mapping intuitive stiffness indices that are extracted from the stiffness matrix. Both the mechanism workspace and stiffness are found to be heavily influenced by cable sagging. The results obtained in this paper support the notion that the effect of cable sagging on a mechanism should be thoroughly assessed prior to pursuing a design based on the assumption of massless cables.

Kinematic analysis and path planning of a new kinematically redundant planar parallel manipulator

SUMMARYIn this work, the 3-RPRR, a new kinematically redundant planar parallel manipulator with six-degrees-of-freedom, is presented. First, the manipulator is introduced and its inverse displacement problem discussed. Then, all types of singularities of the 3-RPRR manipulator are analysed and demonstrated. Thereafter, the dexterous workspace is geometrically obtained and compared with the non-redundant 3-PRR planar parallel manipulator. Finally, based on a geometrical measure of proximity to singular configurations and the condition number of the manipulators' Jacobian matrices, actuation schemes for the manipulators are obtained. Different actuation schemes for a given path are obtained and the quality of their actuation schemes are compared. It is shown that the proposed manipulator is capable of following a path while avoiding the singularities.

3-PRRR redundant planar parallel manipulator: Inverse displacement, workspace and singularity analyses

This paper presents a novel configuration for a kinematically redundant planar parallel manipulator . Advantages of redundant versus non-redundant parallel manipulators are first discussed. The inverse displacement problem is examined, and the workspace of the proposed manipulator is compared to that of a similar-sized non-redundant one. It is shown that both the reachable and dexterous workspaces of the redundant manipulator are significantly larger. The Jacobian matrices of the proposed manipulator are then developed, and the direct and inverse singularities , and the combination of both, are presented. The physical interpretation of each type of singularity is discussed and illustrated.

A Class of Parallel Manipulators Based on Kinematically Simple Branches

Parallel manipulators consisting of serial branches acting in parallel on a common end effector are examined. All nonredundant, six DOF manipulators corresponding to this in-parallel class of structures are enumerated. A specific in-parallel structure, three branches with two actuated joints per branch (3–2,2,2), is chosen as most promising based upon performance considerations. A class of kimematically simple (KS) serial-chain branch joint layouts suitable for the chosen in-parallel structure is defined. Arguments based upon kinematic equivalency of the branches and mobility of the assembled in-parallel manipulator chain are used to show that there exist only five unique branch joint-layouts belonging to the KS class. It is demonstrated that the solution to the inverse displacement problem for in-parallel manipulators based on the KS branches can be expressed in a closed form. Furthermore, the 3–2,2,2 in-parallel manipulators are shown to belong to a family of manipulators whose forward displacement solutions can be resolved through roots of a 16th order polynomial.