Kinematics and Statics Analysis of a 2-DOF Planar Parallel Mechanism with over Constraint

2011 ◽  
Vol 261-263 ◽  
pp. 913-917 ◽  
Author(s):  
Xu Zhao Han ◽  
Yu Mei Huang ◽  
Chun Chen ◽  
Hong Yan Liu ◽  
Xing Fang Yang
Keyword(s):  
Inverse Kinematics ◽  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Virtual Work ◽  
Principle Of Virtual Work ◽  
Real Time Control ◽  
Hybrid Machine Tool ◽  
Time Control ◽  
Solution Equation ◽  
New Type

This paper presents a deep research on 2-DOF planar parallel mechanism during developing a new type of hybrid machine tool. The composition of this planar parallel mechanism is introduced, its direct and inverse kinematics solution equations as well as the solution equations for the speed and the acceleration are deduced, meanwhile, the jacobian matrix is obtained. The statics problems of the parallel mechanism are modeled and analyzed based on principle of virtual work, and the balancing driving force solution equation of the driving part is given. Through the solving process we can see that the direct and inverse solution equations of this mechanism have explicit expressions and convenient to realize real-time control. It forms a solid basis for the design and development of this mechanism.

Inverse Dynamics of a 6-DOF Decoupling Manipulator

2014 ◽  
Author(s):  
Taoran Liu ◽  
Feng Gao ◽  
Xianchao Zhao ◽  
Chenkun Qi
Keyword(s):  
Inverse Kinematics ◽  
Inverse Dynamics ◽  
Virtual Work ◽  
Principle Of Virtual Work ◽  
Real Time Control ◽  
Model Accuracy ◽  
Lower Weight ◽  
Time Control ◽  
Speed Reducer ◽  
Forward And Inverse Kinematics

In this paper, the kinematics and inverse dynamics of a 6-dof full decoupling parallel manipulator is presented. The forward and inverse kinematics solution can be easily obtained and simplify the real-time control due to 6 dof motion full decoupling. Three motors are embedded into the moving platform to realize rotational motion, simple kinematics and isotropic configurations due to the motors and speed reducers have a lower weight. An effective inverse dynamics of the manipulator is derived by the principle of virtual work. The existence of speed reducer for motors have advantages of decreasing mechanical couplings between axes and the full varying inertias are not directly onto each motor output shaft. Since the presence of speed reducer and in order to improve dynamic model accuracy, the inertia of motor rotor-reducer should be computed. Finally, numerical simulation of the inverse dynamics provides that the actuating torques created by gravity, velocity, acceleration and decoupling torque, coupling torque have been computed.

scholarly journals Type Synthesis of 1T2R Parallel Mechanisms Using Structure Coupling-Reducing Method

2019 ◽  
Vol 32 (1) ◽  
Author(s):  
Haitao Liu ◽  
Ke Xu ◽  
Huiping Shen ◽  
Xianlei Shan ◽  
Tingli Yang
Keyword(s):  
Explicit Form ◽  
Parallel Mechanism ◽  
Analytic Solutions ◽  
Forward Kinematics ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Real Time Control ◽  
Time Control ◽  
Topological Characteristics ◽  
Zero Coupling

Abstract Direct kinematics with analytic solutions is critical to the real-time control of parallel mechanisms. Therefore, the type synthesis of a mechanism having explicit form of forward kinematics has become a topic of interest. Based on this purpose, this paper deals with the type synthesis of 1T2R parallel mechanisms by investigating the topological structure coupling-reducing of the 3UPS&UP parallel mechanism. With the aid of the theory of mechanism topology, the analysis of the topological characteristics of the 3UPS&UP parallel mechanism is presented, which shows that there are highly coupled motions and constraints amongst the limbs of the mechanism. Three methods for structure coupling-reducing of the 3UPS&UP parallel mechanism are proposed, resulting in eight new types of 1T2R parallel mechanisms with one or zero coupling degree. One obtained parallel mechanism is taken as an example to demonstrate that a mechanism with zero coupling degree has an explicit form for forward kinematics. The process of type synthesis is in the order of permutation and combination; therefore, there are no omissions. This method is also applicable to other configurations, and novel topological structures having simple forward kinematics can be obtained from an original mechanism via this method.

Development of Equations of Motion for a Stewart Platform Under Prescribed Mount Motion

2018 ◽  
Author(s):  
Takeyuki Ono ◽  
Ryosuke Eto ◽  
Junya Yamakawa ◽  
Hidenori Murakami
Keyword(s):  
Rigid Body ◽  
Virtual Work ◽  
Equations Of Motion ◽  
Base Plate ◽  
Stewart Platform ◽  
Euler Method ◽  
Moving Frame ◽  
Real Time Control ◽  
Precise Positioning ◽  
Time Control

Analytical equations of motion are critical for real-time control of translating manipulators, which require precise positioning of various tools for their mission. Specifically, when manipulators mounted on moving robots or vehicles perform precise positioning of their tools, it becomes economical to develop a Stewart platform, whose sole task is stabilizing the orientation and crude position of its top table, onto which various precision tools are attached. In this paper, analytical equations of motion are developed for a Stewart platform whose motion of the base plate is prescribed. To describe the kinematics of the platform, the moving frame method, presented by one of authors [1,2], is employed. In the method the coordinates of the origin of a body attached coordinate system and vector basis are expressed by using 4 × 4 frame connection matrices, which form the special Euclidean group, SE(3). The use of SE(3) allows accurate description of kinematics of each rigid body using (relative) joint coordinates. In kinetics, the principle of virtual work is employed, in which system virtual displacements are expressed through B-matrix by essential virtual displacements, reflecting the connection of the rigid body system [2]. The resulting equations for fixed base plate reduce to those for the top plate, obtained by the Newton-Euler method. A main result of the paper is the analytical equations of motion in matrix form for dynamics analyses of a Stewart platform whose base plate moves. The control applications of those equations will be deferred to subsequent publications.

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.

Research on 2-Dof Parallel Robot and its Motion Characteristics

2010 ◽  
Vol 139-141 ◽  
pp. 2203-2206
Author(s):  
Hui Ping Shen ◽  
Lei Ding ◽  
Chang Yu Xue ◽  
Ju Li ◽  
Jia Ming Deng ◽  
...  
Keyword(s):  
Real Time ◽  
Industrial Application ◽  
Parallel Mechanism ◽  
Parallel Robot ◽  
Real Time Control ◽  
Time Control ◽  
Surface Welding ◽  
Motion Characteristics ◽  
Straight Lines ◽  
Five Axis

A novel robot, derived from a planar parallel mechanism, is presented. With two sliders driving on the same side of parallel guide rails, this simple but practical mechanism is capable of realizing a large workspace. The direct and inverse kinematical solutions are given. The simulation demonstrates that all kinds of straight lines and circles can be realized by the end actuator of the robot; the corresponding motion disciplines and characteristics driven by the two sliders are analyzed; the results are verified on the prototype. By allowing the end actuator to move in Z-direction or to rotate around A or B-axis, three-, four-, five-axis manipulator would be composed and surface welding and space cutting would be realized. This paper lays the foundation for the real-time control and industrial application of this novel robot.

Redundancy Parameterization for Flexible Motion Control

2010 ◽  
Author(s):  
B. Moore ◽  
E. Oztop
Keyword(s):  
Finite Number ◽  
Inverse Kinematics ◽  
Infinitely Many Solutions ◽  
Redundant Manipulators ◽  
Real Time Control ◽  
End Effector ◽  
Human Control ◽  
Time Control ◽  
Swivel Angle ◽  
Self Motion

Our overall research interest is in synthesizing human like reaching and grasping using anthropomorphic robot hand-arm systems, as well as understanding the principles underlying human control of these actions. When one needs to define the control and task requirements in the Cartesian space, the problem of inverse kinematics needs to be solved. For non-redundant manipulators, a desired end-effector position and orientation can be achieved by a finite number of solutions. For redundant manipulators however, there are in general infinitely many solutions where the cardinality of the solution set must be made finite by imposing certain constraints. In this paper, we consider the Mitsubishi PA10 manipulator which is similar to the human arm, in the sense that both wrist and shoulder joints can be considered to emulate a 3DOF ball joint. We explicitly derive the analytic solution for the inverse kinematics using quaternions. Then, we derive a parameterization in terms of a pure quaternion called the swivel quaternion. The swivel quaternion is similar to the elbow swivel angle used in most approaches, but avoid the computation of inverse trigonometric functions. This parameterization of the self-motion manifold is continuous with any end-effector motion. Given the pose of the end-effector and the swivel quaternion (or swivel angle), the algorithm derives all solution of the inverse kinematics (finite number). We then show how the parameterization of the elbow self-motion can be used for the real-time control of the PA10 manipulator in the presence of obstacles.

Kinematics optimization and static analysis of a modular continuum robot used for minimally invasive surgery

2017 ◽  
Vol 232 (2) ◽  
pp. 135-148 ◽  
Author(s):  
Fei Qi ◽  
Feng Ju ◽  
Dong Ming Bai ◽  
Bai Chen
Keyword(s):  
Minimally Invasive Surgery ◽  
Minimally Invasive ◽  
Invasive Surgery ◽  
Virtual Work ◽  
Structural Parameters ◽  
Real Time Control ◽  
Time Control ◽  
Payload Capacity ◽  
Continuum Robot ◽  
The Relationship

For the outstanding compliance and dexterity of continuum robot, it is increasingly used in minimally invasive surgery. The wide workspace, high dexterity and strong payload capacity are essential to the continuum robot. In this article, we investigate the workspace of a cable-driven continuum robot that we proposed. The influence of section number on the workspace is discussed when robot is operated in narrow environment. Meanwhile, the structural parameters of this continuum robot are optimized to achieve better kinematic performance. Moreover, an indicator based on the dexterous solid angle for evaluating the dexterity of robot is introduced and the distal end dexterity is compared for the three-section continuum robot with different range of variables. Results imply that the wider range of variables achieve the better dexterity. Finally, the static model of robot based on the principle of virtual work is derived to analyze the relationship between the bending shape deformation and the driven force. The simulations and experiments for plane and spatial motions are conducted to validate the feasibility of model, respectively. Results of this article can contribute to the real-time control and movement and can be a design reference for cable-driven continuum robot.

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