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.

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.

A New Approach to Model Constant Curvature Continuum Robot Dynamics

2019 ◽  
Author(s):  
Yujiong Liu ◽  
Pinhas Ben-Tzvi
Keyword(s):  
Constant Curvature ◽  
Inverse Dynamics ◽  
Virtual Work ◽  
Robot Dynamics ◽  
Real Time Control ◽  
Continuum Robots ◽  
New Approach ◽  
Time Control ◽  
Proposed Model ◽  
Vector Representations

Abstract Inspired by nature, continuum robots show their potential in human-centered environments due to the compliant-to-obstacle features and dexterous mobility. However, there are few such robots successfully implemented outside the laboratory so far. One reason is believed to be due to the real time control challenge for soft robots, which require a highly efficient, highly accurate dynamic model. This paper presents a new systematic methodology to formulate the dynamics of constant curvature continuum robots. The new approach builds on several new techniques: 1) using the virtual work principle to formulate the equation of motion, 2) using specifically selected kinematic representations to separate integral variables from the non-integral variables, and 3) using vector representations to put the integral in a compact form. By doing so, the hard-to-solve integrals are evaluated analytically in advance and the accurate inverse dynamics are established accordingly. Numerical simulations are conducted to evaluate the performances of the newly proposed model.

RESEARCH ON RIGID BODY INVERSE DYNAMICS OF A NOVEL 6-PRRS PARALLEL ROBOT

2018 ◽  
Vol 18 (08) ◽  
pp. 1840037
Author(s):  
YUBIN LIU ◽  
GANGFENG LIU
Keyword(s):  
Dynamic Model ◽  
Inverse Dynamics ◽  
Virtual Work ◽  
Equations Of Motion ◽  
Parallel Robot ◽  
Simulation Software ◽  
Real Time Control ◽  
Dynamical Equations ◽  
Time Control ◽  
Systematic Methodology

A systematic methodology for solving the inverse dynamics of a 6-PRRS parallel robot is presented. Based on the principle of virtual work and the Lagrange approach, a methodology for deriving the dynamical equations of motion is developed. To resolve the inconsistency between complications of established dynamic model and real-time control, a simplifying strategy of the dynamic model is presented. The dynamic character of the 6-PRRS parallel robot is analyzed by example calculation, and a full and precise dynamic model using simulation software is established. Verification results show the validity of the presented algorithm, and the simplifying strategies are practical and efficient.

A Parallel, Four Degree-of-Freedom Robotic Wrist

1995 ◽  
Author(s):  
Robert J. Salerno ◽  
Stephen L. Canfield ◽  
Anthony J. Ganino ◽  
Charles F. Reinholtz
Keyword(s):  
Inverse Kinematics ◽  
Parallel Architecture ◽  
High Strength ◽  
Degree Of Freedom ◽  
Real Time Control ◽  
Time Control ◽  
Robot Wrist ◽  
Forward And Inverse Kinematics ◽  
Three Degree Of Freedom ◽  
Robotic Wrist

Abstract Kinematic considerations are presented for a parallel, four degree-of-freedom robot wrist resembling the Clemens coupling, a constant-velocity joint first described in his 1872 patent. In its new form as a wrist, this device provides general orientational mobility as well as axial displacement through a plunge motion. A possibly more important hybrid of this wrist is identified as an artificially constrained, spherical, three degree-of-freedom pitchyaw-roll wrist that can easily be derived from this new concept. Because of its parallel architecture, the new wrist design displays favorable attributes including high strength-to-weight and stiffness-to-weight ratios, a large workspace, and an open center construction. Closed-form forward and inverse kinematics of the wrist are derived for both the three and four degree-of-freedom configurations, thereby making it a likely candidate for real-time control. Workspace plots are also presented that demonstrate the dexterity of the proposed wrist.

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.

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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