A Generalized and Analytical Method to Solve Inverse Kinematics of Serial and Parallel Mechanisms Using Finite Screw Theory

2017 ◽  
pp. 602-608 ◽  
Author(s):  
T. Sun ◽  
S. F. Yang ◽  
T. Huang ◽  
J. S. Dai
Keyword(s):  
Analytical Method ◽  
Inverse Kinematics ◽  
Screw Theory ◽  
Parallel Mechanisms

From Origami to a New Class of Centralized 3-DOF Parallel Mechanisms

2007 ◽  
Author(s):  
Ernesto Rodriguez Leal ◽  
Jian S. Dai
Keyword(s):  
Closed Form ◽  
Inverse Kinematics ◽  
Jacobian Matrix ◽  
Screw Theory ◽  
Geometric Constraints ◽  
Parallel Mechanisms ◽  
Closed Form Solutions ◽  
New Class ◽  
Workspace Analysis ◽  
Inverse Kinematics Problem

This paper applies the ‘technomimetics’ concept to generate a new class of parallel mechanisms inspired by origami folds. This new class of 3-DOF (Degree of Freedom) parallel mechanisms is constructed with 3-RPRP architecture. When the geometric constraints mentioned in this paper are applied, the mechanisms will be allowed to rotate around the x and y axes and translate vertically along the z axis, while the centre of the platform remains concentric to the centre of its base. This paper investigates both position and geometry of these mechanisms and identifies the closed form solutions for the inverse kinematics problem. The differential kinematical analysis is developed by deriving the Jacobian matrix through screw theory and the singularities are identified with workspace analysis. The paper ends with isotropic configuration analysis and illustrates the characteristics of the new mechanisms.

scholarly journals A New Method for Type Synthesis of 2R1T and 2T1R 3-DOF Redundant Actuated Parallel Mechanisms with Closed Loop Units

2020 ◽  
Vol 33 (1) ◽  
Author(s):  
Yongquan Li ◽  
Yang Zhang ◽  
Lijie Zhang
Keyword(s):  
Closed Loop ◽  
Screw Theory ◽  
Line Graph ◽  
Degree Of Freedom ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Allocation Criteria ◽  
Grassmann Line Geometry ◽  
Moving Platform ◽  
Atlas Method

Abstract The current type synthesis of the redundant actuated parallel mechanisms is adding active-actuated kinematic branches on the basis of the traditional parallel mechanisms, or using screw theory to perform multiple getting intersection and union to complete type synthesis. The number of redundant parallel mechanisms obtained by these two methods is limited. In this paper, based on Grassmann line geometry and Atlas method, a novel and effective method for type synthesis of redundant actuated parallel mechanisms (PMs) with closed-loop units is proposed. Firstly, the degree of freedom (DOF) and constraint line graph of the moving platform are determined successively, and redundant lines are added in constraint line graph to obtain the redundant constraint line graph and their equivalent line graph, and a branch constraint allocation scheme is formulated based on the allocation criteria. Secondly, a scheme is selected and redundant lines are added in the branch chains DOF graph to construct the redundant actuated branch chains with closed-loop units. Finally, the branch chains that meet the requirements of branch chains configuration criteria and F&C (degree of freedom & constraint) line graph are assembled. In this paper, two types of 2 rotational and 1 translational (2R1T) redundant actuated parallel mechanisms and one type of 2 translational and 1 rotational (2T1R) redundant actuated parallel mechanisms with few branches and closed-loop units were taken as examples, and 238, 92 and 15 new configurations were synthesized. All the mechanisms contain closed-loop units, and the mechanisms and the actuators both have good symmetry. Therefore, all the mechanisms have excellent comprehensive performance, in which the two rotational DOFs of the moving platform of 2R1T redundant actuated parallel mechanism can be independently controlled. The instantaneous analysis shows that all mechanisms are not instantaneous, which proves the feasibility and practicability of the method.

scholarly journals Sensitivity Analysis of Reliability of Low-Mobility Parallel Mechanisms Based on a Response Surface Method

2021 ◽  
Vol 11 (19) ◽  
pp. 9002
Author(s):  
Qiang Yang ◽  
Hongkun Ma ◽  
Jiaocheng Ma ◽  
Zhili Sun ◽  
Cuiling Li
Keyword(s):  
Sensitivity Analysis ◽  
Response Surface ◽  
Response Surface Method ◽  
Inverse Kinematics ◽  
Parallel Mechanism ◽  
Error Component ◽  
Parallel Mechanisms ◽  
Kinematic Accuracy ◽  
Surface Method ◽  
Input Error

Kinematic accuracy is a crucial indicator for evaluating the performance of mechanisms. Low-mobility parallel mechanisms are examples of parallel robots that have been successfully employed in many industrial fields. Previous studies analyzing the kinematic accuracy analysis of parallel mechanisms typically ignore the randomness of each component of input error, leading to imprecise conclusions. In this paper, we use homogeneous transforms to develop the inverse kinematics models of an improved Delta parallel mechanism. Based on the inverse kinematics and the first-order Taylor approximation, a model is presented considering errors from the kinematic parameters describing the mechanism’s geometry, clearance errors associated with revolute joints and driving errors associated with actuators. The response surface method is employed to build an explicit limit state function for describing position errors of the end-effector in the combined direction. As a result, a mathematical model of kinematic reliability of the improved Delta mechanism is derived considering the randomness of every input error component. And then, reliability sensitivity of the improved Delta parallel mechanism is analyzed, and the influences of the randomness of each input error component on the kinematic reliability of the mechanism are quantitatively calculated. The kinematic reliability and proposed sensitivity analysis provide a theoretical reference for the synthesis and optimum design of parallel mechanisms for kinematic accuracy.

A Simple Method for Inverse Kinematic Analysis of the General 6R Serial Robot

2006 ◽  
Author(s):  
Zhi Xin Shi ◽  
Yu Feng Luo ◽  
Lu Bing Hang ◽  
Ting Li Yang
Keyword(s):  
Kinematic Analysis ◽  
Inverse Kinematics ◽  
Algebraic Method ◽  
Inverse Kinematic ◽  
New Method ◽  
One Dimension ◽  
Parallel Mechanisms ◽  
Simple Method ◽  
Inverse Kinematics Problem ◽  
Serial Robot

Because the solution to inverse kinematics problem of the general 5R serial robot is unique and its assembly condition has been derived, a simple effective method for inverse kinematics problem of general 6R serial robot or forward kinematics problem of general 7R single-loop mechanism is presented based on one-dimension searching algorithm. The new method has the following features: (1) Using one-dimension searching algorithm, all the real inverse kinematic solutions are obtained and it has higher computing efficiency; (2) Compared with algebraic method, it has evidently reduced the difficulty of deducing formulas. The principle of the new method can be generalized to kinematic analysis of parallel mechanisms.

A Method of Inverse Kinematics Solution for a Class of Robotic Manipulators

1997 ◽  
Author(s):  
Tuna Balkan ◽  
M. Kemal Özgören ◽  
M. A. Sahir Arikan ◽  
H. Murat Baykurt
Keyword(s):  
Nonlinear Equation ◽  
Analytical Method ◽  
Multiple Solutions ◽  
Inverse Kinematics ◽  
Industrial Robot ◽  
Robotic Manipulators ◽  
Inverse Kinematic ◽  
Singular Configurations ◽  
Inverse Kinematics Problem ◽  
Joint Variable

Abstract A semi-analytical method and a computer program are developed for inverse kinematics solution of a class of robotic manipulators, in which four joint variables are contained in wrist point equations. For this case, it becomes possible to express all the joint variables in terms of a joint variable, and this reduces the inverse kinematics problem to solving a nonlinear equation in terms of that joint variable. The solution can be obtained by iterative methods and the remaining joint variables can easily be computed by using the solved joint variable. Since the method is manipulator dependent, the equations will be different for kinematically different classes of manipulators, and should be derived analytically. A significant benefit of the method is that, the singular configurations and the multiple solutions indicated by sign ambiguities can be determined while deriving the inverse kinematic expressions. The developed method is applied to a six-revolute-joint industrial robot, FANUC Arc Mate Sr.

scholarly journals Inverse kinematic solution of 6R robot manipulators based on screw theory and the Paden–Kahan subproblem

2018 ◽  
Vol 15 (6) ◽  
pp. 172988141881829 ◽  
Author(s):  
Rongbo Zhao ◽  
Zhiping Shi ◽  
Yong Guan ◽  
Zhenzhou Shao ◽  
Qianying Zhang ◽  
...  
Keyword(s):  
Inverse Kinematics ◽  
Matrix Theory ◽  
Screw Theory ◽  
Robot Manipulator ◽  
Inverse Kinematic ◽  
Kinematic Calibration ◽  
Kinematic Parameters ◽  
Kinematics Modeling ◽  
High Level ◽  
Kinematic Solution

The traditional Denavit–Hatenberg method is a relatively mature method for modeling the kinematics of robots. However, it has an obvious drawback, in that the parameters of the Denavit–Hatenberg model are discontinuous, resulting in singularity when the adjacent joint axes are parallel or close to parallel. As a result, this model is not suitable for kinematic calibration. In this article, to avoid the problem of singularity, the product of exponentials method based on screw theory is employed for kinematics modeling. In addition, the inverse kinematics of the 6R robot manipulator is solved by adopting analytical, geometric, and algebraic methods combined with the Paden–Kahan subproblem as well as matrix theory. Moreover, the kinematic parameters of the Denavit–Hatenberg and the product of exponentials-based models are analyzed, and the singularity of the two models is illustrated. Finally, eight solutions of inverse kinematics are obtained, and the correctness and high level of accuracy of the algorithm proposed in this article are verified. This algorithm provides a reference for the inverse kinematics of robots with three adjacent parallel joints.

The Algorithm of Redundant Robotic Kinematics Based on Exponential Product

2011 ◽  
Vol 58-60 ◽  
pp. 1902-1907 ◽  
Author(s):  
Xin Fen Ge ◽  
Jing Tao Jin
Keyword(s):  
Real Time ◽  
Inverse Kinematics ◽  
Screw Theory ◽  
Product Formula ◽  
Real Time Control ◽  
Time Control ◽  
Direct Kinematics ◽  
Product Formulas

The intrinsically redundant series manipulator’s kinematics were studied by the exponential product formula of screw theory, the direct kinematics problem and Inverse kinematics problems were analyzed, and the intrinsically redundant series manipulator’s kinematics solution that based on exponential product formulas were proposed; the intrinsically redundant series manipulator’s kinematics is decomposed into several simple sub-problems, then analyzed sub-problem, and set an example to validate the correctness of the proposed method. Finally, comparing the exponential product formula and the D-H parameters, draw that they are essentially the same in solving the manipulator’s kinematics, so as to the algorithm of the manipulator’s kinematics based on exponential product formulas are correct, and the manipulator’s kinematics process based on exponential product formula is more simple and easier to real-time control of industrial.

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