Design, kinematic and dynamic modeling of a novel tripod based manipulator

Robotica ◽  
2014 ◽  
Vol 34 (10) ◽  
pp. 2186-2204 ◽  
Author(s):  
Dan Zhang ◽  
Bin Wei
Keyword(s):  
Set Theory ◽  
Dynamic Modeling ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
General Function ◽  
Multi Objective Optimization ◽  
Gf Set ◽  
Hybrid Manipulator ◽  
New Type ◽  
Three Degrees Of Freedom

SUMMARYThis paper proposes a novel three-degrees-of-freedom (3-DOF) hybrid manipulator, 3PU*S-PU, which evolves from the general function (Gf) set theory. After discussing the advantages of this new type of hybrid manipulator, this report analyzes the kinematic and Jacobian matrix of the manipulator. Subsequently, the kinematic performances, including stiffness/compliance, and workspace, undergo analysis, followed by the multi-objective optimization of the compliance and workspace. The Lagrangian method provides the framework for briefly analyzing the dynamics of the proposed manipulator. Finally, the results of this assessment comprise a guideline for controlling the manipulator.

Experimental and Numerical Hydrodynamic Modeling of an Underwater Manipulator

2001 ◽  
Author(s):  
A. Khanicheh ◽  
A. Tehranian ◽  
A. Meghdari ◽  
M. S. Sadeghipour
Keyword(s):  
Drag Coefficient ◽  
Dynamic Modeling ◽  
Hydrodynamic Model ◽  
Degrees Of Freedom ◽  
Added Mass ◽  
Hydrodynamic Modeling ◽  
Degree Of Freedom ◽  
Experimental Results ◽  
Underwater Manipulator ◽  
Three Degrees Of Freedom

Abstract This paper presents the kinematics and dynamic modeling of a three-link (3-DOF) underwater manipulator where the effects of hydrodynamic forces are investigated. In our investigation, drag and added mass coefficients are not considered as constants. In contrast, the drag coefficient is a variable with respect to all relative parameters. Experiments were conducted to validate the hydrodynamic model for a one degree-of-freedom manipulator up to a three degrees-of-freedom manipulator. Finally, the numerical and experimental results are compared and thoroughly discussed.

Architecture Optmization of a 3-DOF Parallel Mechanism

1998 ◽  
Author(s):  
J. A. Carretero ◽  
R. P. Podhorodeski ◽  
M. Nahon
Keyword(s):  
Parallel Mechanism ◽  
Architectural Design ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Design Parameters ◽  
Objective Functions ◽  
Constraint Equations ◽  
Three Degree Of Freedom ◽  
Architecture Optimization ◽  
Three Degrees Of Freedom

Abstract This paper presents a study of the architecture optimization of a three-degree-of-freedom parallel mechanism intended for use as a telescope mirror focussing device. The construction of the mechanism is first described. Since the mechanism has only three degrees of freedom, constraint equations describing the inter-relationship between the six Cartesian coordinates are given. These constraints allow us to define the parasitic motions and, if incorporated into the kinematics model, a constrained Jacobian matrix can be obtained. This Jacobian matrix is then used to define a dexterity measure. The parasitic motions and dexterity are then used as objective functions for the optimizations routines and from which the optimal architectural design parameters are obtained.

Fully-Isotropic T1R2-Type Parallel Robots With Three Degrees of Freedom

2005 ◽  
Author(s):  
Grigore Gogu
Keyword(s):  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Parallel Robots ◽  
Velocity Space ◽  
Linear Transformations ◽  
Matrix Mapping ◽  
Joint Velocity ◽  
First Time ◽  
Three Degrees Of Freedom

The paper presents singularity-free fully-isotropic T1R2-type parallel manipulators (PMs) with three degrees of freedom. The mobile platform has one independent translation (T1) and two rotations (R2). A method is proposed for structural synthesis of fully-isotropic T1R2-type PMs based on the theory of linear transformations. A one-to-one correspondence exists between the actuated joint velocity space and the external velocity space of the moving platform. The Jacobian matrix mapping the two vector spaces of fully-isotropic T1R2-type PMs presented in this paper is the 3x3 identity matrix throughout the entire workspace. The condition number and the determinant of the Jacobian matrix being equal to one, the manipulator performs very well with regard to force and motion transmission capabilities. As far as we are aware, this paper presents for the first time in the literature solutions of singularity-free T1R2-type PMs with decoupled an uncoupled motions, along with the fully-isotropic solutions.

Fully-Isotropic Redundantly-Actuated Parallel Wrists With Three Degrees of Freedom

2007 ◽  
Author(s):  
Grigore Gogu
Keyword(s):  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Velocity Space ◽  
Structural Synthesis ◽  
Linear Transformations ◽  
Force And Motion ◽  
Redundantly Actuated ◽  
Joint Velocity ◽  
First Time ◽  
Three Degrees Of Freedom

The paper presents fully-isotropic redundantly-actuated parallel wrists (RaPWs) with three degrees of freedom. The mobile platform has three independent rotations. A method is proposed for structural synthesis of fully-isotropic RaPWs based on the theory of linear transformations. A one-to-one correspondence exists between the actuated joint velocity space and the external velocity space of the moving platform. The Jacobian mapping the two vector spaces of fully-isotropic RaPWs presented in this paper is 3×3 identity matrix throughout the entire workspace. The condition number and the determinant of the Jacobian matrix being equal to one, the manipulator performs very well with regard to force and motion transmission capabilities. Redundant actuation is used to obtain fully-isotropic parallel wrists with three degrees of freedom. As far as we are aware, this paper presents for the first time in the literature the use of redundancy to design fully-isotropic parallel wrists as well as solutions of fullyisotropic RaPWs with three degrees of freedom.

scholarly journals An investigation on kinematics and dynamics performance of a novel 3-PRC-compliant parallel micromanipulator

2018 ◽  
Vol 10 (7) ◽  
pp. 168781401878980 ◽  
Author(s):  
Xiang-Chun Li ◽  
Yangmin Li ◽  
Bing-Xiao Ding ◽  
Hong-Ye Xu
Keyword(s):  
Piezoelectric Actuator ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Lagrange Equation ◽  
Kinematics And Dynamics ◽  
Vector Method ◽  
Kinematics Model ◽  
New Type ◽  
Amplification Mechanism

This article proposes a 3-PRC compliant parallel micromanipulator with 3 degrees of freedom. The piezoelectric actuator is adopted to drive the mechanism, and to compensate the stroke of the piezoelectric actuator, a new type of secondary lever amplification mechanism is designed. The kinematics model of the 3-PRC parallel micromanipulation platform is derived using vector method, and the forward and inverse kinematics solutions of a 3-PRC parallel micromanipulation stage are emphatically analyzed and then the Jacobian matrix of kinematics model and workspace are derived. Finally, the dynamic model is established by Lagrange equation, and the natural frequency of the mechanism is calculated. The modal analysis is carried out using finite element method. The results showed that the mechanism has a favorable performance on kinematics and dynamics, and this micromanipulator can achieve micro/nano level motion with high accuracy.

Dynamic Modeling of the Three-Degrees-of-Freedom Planar Platform-Type Manipulator

1997 ◽  
Author(s):  
Maher G. Mohamed ◽  
Hazem A. Attia
Keyword(s):  
Dynamic Modeling ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Open Loop ◽  
Loop System ◽  
Constraint Forces ◽  
Open Loop System ◽  
Joint Coordinates ◽  
Joint Constraints ◽  
Three Degrees Of Freedom

Abstract In this paper, the dynamic Modeling of the planar three-degrees of freedom platform-type manipulator is presented. A kinematic analysis is carried out initially, to evaluate and correct the initial coordinates and velocities. The dynamic model of the manipulator is formulated using a two-step transformation. Initially, the dynamic formulation is written in terms of the Cartesian coordinates of a dynamically equivalent system of particles. Since a particle does not have rotational motion, the differential equations of motion are derived by applying Newton’s second law to study the translational motion of the particles. A system of nine primary particles replaces the whole manipulator and the system mass matrix is derived. The equations of motion are then transformed to a more manipulator oriented variables; relative joint coordinates. This leads to efficient solution and integration of the equations of motion. Since the multibody system under consideration contains two independent closed kinematic loops, each of the two closed loops is cut at a suitable joints in order to produce a reduced open loop system with additional constraint equations. When the two cut joints are reassembled, the defined relative joint coordinates are no longer independent. They are related by the cut joint constraints. The constraint forces associated with the cut joint constraints are expressed in terms of Lagrange multipliers. Both cut joint constraints and constraint forces are then introduced into the equations of motion for the reduced open loop system to produce the resulting equations of motions of manipulator. A numerical example is presented and a computer program is developed.

Kinematic Analysis of a Three-DOF Parallel Mechanism for Telescope Applications

1997 ◽  
Author(s):  
J. A. Carretero ◽  
M. Nahon ◽  
B. Buckham ◽  
C. M. Gosselin
Keyword(s):  
Kinematic Analysis ◽  
Inverse Kinematics ◽  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Constraint Equations ◽  
Forward And Inverse Kinematics ◽  
Position And Orientation ◽  
Three Degree Of Freedom ◽  
Three Degrees Of Freedom

Abstract This paper presents a kinematic analysis of a three-degree-of-freedom parallel mechanism intended for use as a telescope mirror focussing device. The construction of the mechanism is first described and its forward and inverse kinematics solutions are derived. Because the mechanism has only three degrees of freedom, constraint equations must be generated to describe the inter-relationship between the six Cartesian coordinates which describe the position and orientation of the moving platform. Once these constraints are incorporated into the kinematics model, a constrained Jacobian matrix is obtained. The stiffness and dexterity properties of the mechanism are then determined based on this Jacobian matrix. The mechanism is shown to exhibit desirable properties in the region of its workspace of interest in the telescope focussing application.

Continuous motion of a novel 3-CRC symmetrical parallel mechanism

2015 ◽  
Vol 230 (3) ◽  
pp. 392-405 ◽  
Author(s):  
Ziming Chen ◽  
Wen-ao Cao ◽  
Huafeng Ding ◽  
Zhen Huang
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Parallel Mechanisms ◽  
Numerical Examples ◽  
Parasitic Motion ◽  
Continuous Rotation ◽  
Moving Platform ◽  
Motion Characteristics ◽  
Three Degrees Of Freedom

Parallel mechanisms (PMs) with three degrees of freedom (DOFs) have been studied extensively, especially the PMs with two rotational and one translational DOFs (2R1T PMs). One major problem of the 2R1T PMs is the inherent parasitic motion. In this paper, a novel 2R1T symmetrical parallel mechanism with no parasitic motion is proposed and studied. The moving platform and the base of this mechanism are mirror symmetric with respect to a mid-plane. This moving platform can realize continuous rotation about any axis or any point on the mid-plane and can have continuous translation along the normal line of the mid-plane. The constraint and motion characteristics of this mechanism are analyzed. The kinematics solutions and the Jacobian matrix are derived. The singularities of this PM are discussed. In the end, several numerical examples are given to show the continuous rotations and continuous translations of this PM. This kind of PMs has outstanding advantages of easy path planning and controlling.

Dynamic Modeling and Analysis for a Planar Three Degrees-of-Freedom Manipulator Under Prescribed Mount Motion

2019 ◽  
Author(s):  
Takeyuki Ono ◽  
Ryosuke Eto ◽  
Junya Yamakawa ◽  
Hidenori Murakami
Keyword(s):  
Dynamic Modeling ◽  
Degrees Of Freedom ◽  
Sliding Mode ◽  
Virtual Work ◽  
Equations Of Motion ◽  
Base Plate ◽  
Moving Frame ◽  
Parallel Plates ◽  
Modeling And Analysis ◽  
Three Degrees Of Freedom

Abstract This paper presents dynamic modeling of a planar, three degrees-of-freedom manipulator consisting of two parallel plates, referred to as top and base plates, which are connected by three actuated legs. When a sensitive equipment is carried by a moving robot or vehicle, it becomes necessary to mount the equipment on a platform which achieves precise positioning for stabilization. The objectives of this paper are to derive analytical equations of motion and apply them to control simulations on the stabilizing planar manipulator. In the derivation of analytical equations of motion, the moving frame method is utilized to describe the kinematics of the two-dimensional multibody system. For the manipulator system comprised of jointed bodies, a graph tree is utilized, which visually illustrates how the constituent bodies are connected to each other. For kinetics, the principle of virtual work is employed to derive the analytical equations of motion for the manipulator system. The resulting equations of motion are used to numerically assess the performance of a sliding mode controller (SMC) to stabilize the top plate from the motion of the translating and rotating base plate. In the numerical simulation, the SMC is compared with a simple PID controller to evaluate both the tracking performance and robustness.

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