scholarly journals Closed-Form Direct Kinematics Solution of a New Parallel Minimanipulator

1994 ◽  
Vol 116 (4) ◽  
pp. 1141-1147 ◽  
Author(s):  
F. Tahmasebi ◽  
L.-W. Tsai
Keyword(s):  
Closed Form ◽  
Inverse Kinematics ◽  
Kinematics Analysis ◽  
Degree Polynomial ◽  
Half Angle ◽  
Kinematic Inversion ◽  
Plane Passing ◽  
Moving Platform ◽  
Six Degree Of Freedom ◽  
Direct Kinematics

Closed-form direct kinematics solution of a new three-limbed six-degree-of-freedom minimanipulator is presented. Five-bar linkages and inextensible limbs are used in synthesis of the minimanipulator to improve its positional resolution and stiffness. All of the minimanipulator actuators are base-mounted. Kinematic inversion is used to reduce the direct kinematics of the mimimanipulator to an eighth-degree polynomial in the square of tangent of half-angle between one of the limbs and the moving platform. Hence, the maximum number of assembly configurations for the minimanipulator is sixteen. Furthermore, it is proved that the sixteen solutions are eight pairs of reflected configurations with respect to the plane passing through the lower ends of the three limbs. A numerical example is also presented and the results are verified by an inverse kinematics analysis.

Kinematics of a New High-Precision Three-Degree-of-Freedom Parallel Manipulator

2006 ◽  
Vol 129 (3) ◽  
pp. 320-325 ◽  
Author(s):  
Farhad Tahmasebi
Keyword(s):  
Power Dissipation ◽  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Degree Of Freedom ◽  
Base Plane ◽  
Degree Polynomial ◽  
Payload Capacity ◽  
Half Angle ◽  
Three Degree Of Freedom ◽  
Direct Kinematics

Closed-form direct and inverse kinematics of a new three-degree-of-freedom (DOF) parallel manipulator with inextensible limbs and base-mounted actuators are presented. The manipulator has higher resolution and precision than the existing three-DOF mechanisms with extensible limbs. Since all of the manipulator actuators are base mounted, higher payload capacity, smaller actuator sizes, and lower power dissipation can be obtained. The manipulator is suitable for alignment applications where only tip, tilt, and piston motions are significant. The direct kinematics of the manipulator is reduced to solving an eighth-degree polynomial in the square of the tangent of the half-angle between one of the limbs and the base plane. Hence, there are at most 16 assembly configurations for the manipulator. In addition, it is shown that the 16 solutions are eight pairs of reflected configurations with respect to the base plane. Numerical examples for the direct and inverse kinematics of the manipulator are also presented.

Kinematics of a New High Precision Three Degree-of-Freedom Parallel Manipulator

2005 ◽  
Author(s):  
Farhad Tahmasebi
Keyword(s):  
Power Dissipation ◽  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Degree Of Freedom ◽  
Base Plane ◽  
Degree Polynomial ◽  
Payload Capacity ◽  
Half Angle ◽  
Three Degree Of Freedom ◽  
Direct Kinematics

Closed-form direct and inverse kinematics of a new three degree-of-freedom (DOF) parallel manipulator with inextensible limbs and base-mounted actuators are presented. The manipulator has higher resolution and precision than the existing three DOF mechanisms with extensible limbs. Since all of the manipulator actuators are base-mounted; higher payload capacity, smaller actuator sizes, and lower power dissipation can be obtained. The manipulator is suitable for alignment applications where only tip, tilt, and piston motions are significant. The direct kinematics of the manipulator is reduced to solving an eighth-degree polynomial in the square of tangent of half-angle between one of the limbs and the base plane. Hence, there are at most sixteen assembly configurations for the manipulator. In addition, it is shown that the sixteen solutions are eight pairs of reflected configurations with respect to the base plane. Numerical examples for the direct and inverse kinematics of the manipulator are also presented.

scholarly journals IKBT: Solving Symbolic Inverse Kinematics with Behavior Tree (Extended Abstract)

2020 ◽  
Author(s):  
Dianmu Zhang ◽  
Blake Hannaford
Keyword(s):  
Closed Form ◽  
Inverse Kinematics ◽  
Intelligent System ◽  
Logical Reasoning ◽  
Robot Arm ◽  
Kinematics Analysis ◽  
Closed Form Solutions ◽  
Behavior Tree ◽  
Behavior Trees ◽  
High Level

Inverse kinematics solves the problem of how to control robot arm joints to achieve desired end effector positions, which is critical to any robot arm design and implementations of control algorithms. It is a common misunderstanding that closed-form inverse kinematics analysis is solved. Popular software and algorithms, such as gradient descent or any multi-variant equations solving algorithm, claims solving inverse kinematics but only on the numerical level. While the numerical inverse kinematics solutions are relatively straightforward to obtain, these methods often fail, even when the inverse kinematics solutions exist. Therefore, closed-form inverse kinematics analysis is superior, but there is no generalized automated algorithm. Up till now, the high-level logical reasoning involved in solving closed-form inverse kinematics made it hard to automate, so it's handled by human experts. We developed IKBT, a knowledge-based intelligent system that can mimic human experts' behaviors in solving closed-from inverse kinematics using Behavior Tree. Knowledge and rules used by engineers when solving closed-from inverse kinematics are encoded as actions in Behavior Tree. The order of applying these rules is governed by higher level composite nodes, which resembles the logical reasoning process of engineers. It is also the first time that the dependency of joint variables, an important issue in inverse kinematics analysis, is automatically tracked in graph form. Besides generating closed-form solutions, IKBT also explains its solving strategies in human (engineers) interpretable form. This is a proof-of-concept of using Behavior Trees to solve high-cognitive problems.

scholarly journals Kinematics Simulation of Gough-Stewart Parallel Manipulator by Using Simulink Package in Matlab Software

2019 ◽  
Vol 27 (2) ◽  
pp. 10-20
Author(s):  
Hassan Mohammed Alwan ◽  
Riyadh Ahmed Sarhan
Keyword(s):  
Theoretical Model ◽  
Parallel Manipulator ◽  
Degree Of Freedom ◽  
Kinematics Analysis ◽  
Matlab Software ◽  
Kinematics Simulation ◽  
Moving Platform ◽  
Position And Orientation ◽  
Six Degree Of Freedom ◽  
Forward Equations

The Gough Stewart Robotic manipulator is a parallel manipulator with six-degree of freedom, which has six equations of Kinematics (Inverse and forward), with six variables (Lengths, Position, and Orientation). In this work derived the inverse equations, which used to compute the lengths of the linkages and its changes depended on the position and orientation of the platform's center, then derived the forward equations to calculate the position and orientation of the moving platform in terms of the lengths. This theoretical model of the kinematics analysis of the Gough Stewart has been built into the Simulink package in Matlab to obtain the lengths, position, and orientation for the manipulator at any time of motion. The input parameters (Position and Orientation) in inverse blocks compared with the output parameters (Position and Orientation) in the forward blocks, which show good results.

scholarly journals A Six Degree of Freedom Epicyclic-Parallel Manipulator

2012 ◽  
Vol 4 (4) ◽  
Author(s):  
Chao Chen ◽  
Thibault Gayral ◽  
Stéphane Caro ◽  
Damien Chablat ◽  
Guillaume Moroz ◽  
...  
Keyword(s):  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Degree Of Freedom ◽  
Kinematics Analysis ◽  
End Effector ◽  
Six Dof ◽  
Six Degree Of Freedom

A new six-dof epicyclic-parallel manipulator with all actuators allocated on the ground is introduced. It is shown that the system has a considerably simple kinematics relationship, with the complete direct and inverse kinematics analysis provided. Further, the first and second links of each leg can be driven independently by two motors. The serial and parallel singularities of the system are determined, with an interesting feature of the system being that the parallel singularity is independent of the position of the end-effector. The workspace of the manipulator is also analyzed with future applications in haptics in mind.

scholarly journals Freeing the Serial Mechanism Designer from Inverse Kinematic Solvability Constraints

2010 ◽  
Vol 7 (3) ◽  
pp. 209-216 ◽  
Author(s):  
Diana C. W. Friedman ◽  
Tim Kowalewski ◽  
Radivoje Jovanovic ◽  
Jacob Rosen ◽  
Blake Hannaford
Keyword(s):  
Patient Safety ◽  
Robotic Surgery ◽  
Closed Form ◽  
Inverse Kinematics ◽  
Inverse Kinematic ◽  
Forward Kinematics ◽  
Joint Angles ◽  
Computing Power ◽  
Six Degree Of Freedom ◽  
Serial Mechanism

This paper presents a fast numerical solution for the inverse kinematics of a serial manipulator. The method is implemented on the C-arm, a manipulator designed for use in robotic surgery. The inverse kinematics solution provides all possible solutions for any six degree-of-freedom serial manipulator, assuming that the forward kinematics are known and that it is possible to solve for the remaining joint angles if one joint angle’s value is known. With a fast numerical method and the current levels of computing power, designing a manipulator with closed-form inverse kinematics is no longer necessary. When designing the C-arm, we therefore chose to weigh other factors, such as actuator size and patient safety, more heavily than the ability to find a closed-form inverse kinematics solution.

The Inverse Force Analysis of a Four-Bar Mechanism With Compliant Input and Output Links

1996 ◽  
Author(s):  
J. P. Yin ◽  
G. K. Matthew ◽  
J. Duffy
Keyword(s):  
Closed Form ◽  
Angular Displacement ◽  
Force Analysis ◽  
Output Link ◽  
Degree Polynomial ◽  
Numerical Result ◽  
Input And Output ◽  
Half Angle ◽  
Inverse Force

Abstract A closed-form inverse force analysis was performed for a planar four-bar mechanism with a rigid coupler and frame but with compliance in the form of linear springs in the input and output links. A known force was applied to the coupler link on a line fixed in the plane containing the frame. A sixteenth degree polynomial in the tan-half-angle of the angular displacement of the output link was derived using algebraic elimination. A numerical result is presented which verifies the solutions.

scholarly journals IKBT: Solving Symbolic Inverse Kinematics with Behavior Tree

2019 ◽  
Vol 65 ◽  
pp. 457-486 ◽  
Author(s):  
Dianmu Zhang ◽  
Blake Hannaford
Keyword(s):  
Closed Form ◽  
Inverse Kinematics ◽  
Intelligent System ◽  
Logical Reasoning ◽  
Robot Arm ◽  
Kinematics Analysis ◽  
Closed Form Solutions ◽  
Behavior Tree ◽  
Behavior Trees ◽  
High Level

Inverse kinematics solves the problem of how to control robot arm joints to achieve desired end effector positions, which is critical to any robot arm design and implementations of control algorithms. It is a common misunderstanding that closed-form inverse kinematics analysis is solved. Popular software and algorithms, such as gradient descent or any multi-variant equations solving algorithm, claims solving inverse kinematics but only on the numerical level. While the numerical inverse kinematics solutions are relatively straightforward to obtain, these methods often fail, due to dependency on specific numerical values, even when the inverse kinematics solutions exist. Therefore, closed-form inverse kinematics analysis is superior, but there is no generalized automated algorithm. Up till now, the high-level logical reasoning involved in solving closed-form inverse kinematics made it hard to automate, so it's handled by human experts. We developed IKBT, a knowledge-based intelligent system that can mimic human experts' behaviors in solving closed-from inverse kinematics using Behavior Tree. Knowledge and rules used by engineers when solving closed-from inverse kinematics are encoded as actions in Behavior Tree. The order of applying these rules is governed by higher level composite nodes, which resembles the logical reasoning process of engineers. It is also the first time that the dependency of joint variables, an important issue in inverse kinematics analysis, is automatically tracked in graph form. Besides generating closed-form solutions, IKBT also explains its solving strategies in human (engineers) interpretable form. This is a proof-of-concept of using Behavior Trees to solve high-cognitive problems.

Kinematics Analysis of a Novel 5-DOF Hybrid Manipulator

2015 ◽  
Vol 9 (6) ◽  
pp. 765-774 ◽  
Author(s):  
Wanjin Guo ◽  
◽  
Ruifeng Li ◽  
Chuqing Cao ◽  
Yunfeng Gao ◽  
...  
Keyword(s):  
Closed Form ◽  
Inverse Kinematics ◽  
Closed Form Solution ◽  
Form Solution ◽  
Parallel Mechanisms ◽  
Kinematics Analysis ◽  
Structure And Motion ◽  
Reachable Workspace ◽  
Hybrid Manipulator ◽  
Inverse Kinematics Problem

Application of hybrid robotics is a continuously developing field, as hybrid manipulators have demonstrated that they can combine the benefits of serial structures and parallel mechanisms. In this paper, a novel 5-degree-of-freedom hybrid manipulator is designed. The structure of this manipulator and its kinematics analysis are presented. An innovative closed-form solution was proposed to address the inverse kinematics problem. Additionally, the validity of the closed-form solution was verified via co-simulation using MATLAB and ADAMS. Finally, the reachable workspace of this manipulator was obtained for further optimizing the structure and motion control.

scholarly journals Kinematics Analysis of a Novel Five-Degree-of-Freedom Spatial Parallel Micromanipulator

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Daniel Prusak ◽  
Konrad Kobus ◽  
Grzegorz Karpiel
Keyword(s):  
Mathematical Model ◽  
Piezoelectric Actuator ◽  
Analytical Solutions ◽  
Inverse Kinematics ◽  
Geometrical Model ◽  
Degree Of Freedom ◽  
Kinematics Analysis ◽  
Moving Platform ◽  
Position And Orientation ◽  
The Mathematical Model

A study of the inverse kinematics for a five-degree-of-freedom (DOF) spatial parallel micromanipulator is presented here below. The objective of this paper is the introduction of a structural and geometrical model of a novel five-degree-of-freedom spatial parallel micromanipulator, analysis of the effective and useful workspace of the micromechanism, presentation of the obtained analytical solutions of the microrobot’s inverse kinematics tasks, and verification of its correctness using selected computer programs and computation environments. The mathematical model presented in this paper describes the behaviour of individual elements for the applied 2-DOF novel piezoelectric actuator, resulting from the position and orientation of the microrobot’s moving platform.

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