Kinematic Analysis of a Novel Translational Platform

2003 ◽  
Vol 125 (2) ◽  
pp. 308-315 ◽  
Author(s):  
Massimo Callegari ◽  
Matteo Tarantini
Keyword(s):  
Closed Form ◽  
Kinematic Analysis ◽  
Parallel Mechanism ◽  
Simple Structure ◽  
Jacobian Matrix ◽  
Differential Analysis ◽  
Symbolic Expression ◽  
Closed Form Solutions ◽  
Design Considerations ◽  
Working Space

A new three-d.o.f. parallel mechanism, with 3-RPC topology, is presented in the paper and its kinematics is studied. The proposed architecture, if proper geometrical conditions are satisfied, has an overconstrained structure which allows motions of pure translation. The simple structure of the mechanism allows finding closed-form solutions for both inverse and direct position kinematics; the differential analysis has been developed as well, by deriving a symbolic expression for the Jacobian matrix. Then, some design considerations are exposed to keep the singular points out of the working space of the mechanism and all the isotropic configurations are eventually identified.

On the kinematics of a new parallel mechanism with Schoenflies motion

Robotica ◽  
2015 ◽  
Vol 34 (9) ◽  
pp. 2056-2070 ◽  
Author(s):  
Po-Chih Lee ◽  
Jyh-Jone Lee
Keyword(s):  
Closed Form ◽  
Condition Number ◽  
Kinematic Analysis ◽  
Parallel Mechanism ◽  
Parallel Manipulator ◽  
Matrix Algebra ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Pick And Place

SUMMARYThis paper investigates the kinematics of one new isoconstrained parallel manipulator with Schoenflies motion. This new manipulator has four degrees of freedom and two identical limbs, each having the topology of Cylindrical–Revolute–Prismatic–Helical (C–R–P–H). The kinematic equations are derived in closed-form using matrix algebra. The Jacobian matrix is then established and the singularities of the robot are investigated. The reachable workspaces and condition number of the manipulator are further studied. From the kinematic analysis, it can be shown that the manipulator is simple not only for its construction but also for its control. It is hoped that the results of the evaluation of the two-limb parallel mechanism can be useful for possible applications in industry where a pick-and-place motion is required.

An Automated Inversion Apporach to Closed-Form Kinematic Analysis of Planar Mechanisms

1992 ◽  
Author(s):  
Arunava Biswas ◽  
Gary L. Kinzel
Keyword(s):  
Closed Form ◽  
Iterative Methods ◽  
Kinematic Analysis ◽  
Equation Approach ◽  
Planar Mechanisms ◽  
Loop Equation ◽  
Closed Form Solutions

Abstract In this paper an inversion approach is developed for the analysis of planar mechanisms using closed-form equations. The vector loop equation approach is used, and the occurrence matrices of the variables in the position equations are obtained. After the loop equations are formed, dependency checking of the unknowns is performed to determine if it is possible to solve for any two equations in two unknowns. For the cases where the closed-form solutions cannot be implemented directly, possible inversions of the mechanism are studied. If the vector loop equations for an inversion can be solved in closed-form, they are identified and solved, and the solutions are transformed back to the original linkage. The method developed in this paper eliminates the uncertainties involved, and the large number of computations required in solving the equations by iterative methods.

Geometry and Kinematic Analysis of a Redundantly Actuated Parallel Mechanism for Rehabilitation

2007 ◽  
Author(s):  
Jody A. Saglia ◽  
Jian S. Dai
Keyword(s):  
Control System ◽  
Kinematic Analysis ◽  
Parallel Mechanism ◽  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Forward Kinematics ◽  
Control System Design ◽  
Ankle Rehabilitation ◽  
Redundantly Actuated ◽  
Moving Platform

This paper presents the geometry and the kinematic analysis of a parallel manipulator developed for ankle rehabilitation, as the beginning of a control system design process. First the geometry of the parallel mechanism is described, secondly the equations for the inverse and the forward kinematics are obtained, then the forward kinematics is analyzed in order to define all the possible configurations of the moving platform. Finally the Jacobian matrix of the rig is obtained by differentiating the position equations and the singularities are investigated, comparing the non-redundant and redundant type of mechanism.

KINEMATIC ANALYSIS AND PROTOTYPE OF A METAMORPHIC ANTHROPOMORPHIC HAND WITH A RECONFIGURABLE PALM

2011 ◽  
Vol 08 (03) ◽  
pp. 459-479 ◽  
Author(s):  
GUOWU WEI ◽  
JIAN S. DAI ◽  
SHUXIN WANG ◽  
HAIFENG LUO
Keyword(s):  
Closed Form ◽  
Matrix Equation ◽  
Kinematic Analysis ◽  
Structure Design ◽  
Characteristic Matrix ◽  
Robotic Hand ◽  
Closed Form Solutions ◽  
First Time

A novel metamorphic anthropomorphic hand is for the first time introduced in this paper. This robotic hand has a reconfigurable palm that generates changeable topology and augments dexterity and versatility of the hand. Structure design of the robotic hand is presented and based on mechanism decomposition kinematics of the metamorphic anthropomorphic hand is characterized with closed-form solutions leading to the workspace investigation of the robotic hand. With characteristic matrix equation, twisting motion of the metamorphic robotic hand is investigated to reveal both dexterity and manipulability of the metamorphic hand. Through a prototype, grasping and prehension of the robotic hand are tested to illustrate characteristics of the new metamorphic anthropomorphic hand.

Optimal design of a micro parallel positioning platform. Part I: Kinematic analysis

Robotica ◽  
2004 ◽  
Vol 22 (6) ◽  
pp. 599-609 ◽  
Author(s):  
Kun-Ku Oh ◽  
Xin-Jun Liu ◽  
Deuk Soo Kang ◽  
Jongwon Kim
Keyword(s):  
Kinematic Analysis ◽  
Inverse Kinematics ◽  
Jacobian Matrix ◽  
High Mobility ◽  
Working Space ◽  
System A ◽  
Capability Analysis ◽  
Dual Stage ◽  
Stage System ◽  
Three Degree Of Freedom

Using a coarse-and-fine actuator combination (dual stage system), a new design of the three degree-of-freedom (DOF) micro parallel positioning platform with high mobility, high accuracy, and a large working space is proposed. To achieve these three DOFs and implement the dual stage system, there are six possible architectures for the coarse and fine actuators, respectively. This paper is organized in two parts. Part I treats the kinematic analysis of each architecture and the problem of selecting the correct coarse actuator architecture. Inverse kinematics and Jacobian matrices for six types of coarse actuator architectures are derived and one proper coarse actuator architecture is selected based on the mobility (rotational capability) analysis, condition number evaluation of the Jacobian matrix, and manufacturability consideration. Part II on real machine design will follow in the next issue of Robotica.

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.

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.

Kinematic Analysis and Design of 3-RPSR Parallel Mechanism with Triple Revolute Joints on the Base

2010 ◽  
Vol 4 (4) ◽  
pp. 346-354 ◽  
Author(s):  
Yukio Takeda ◽  
◽  
Xiao Xiao ◽  
Kazuya Hirose ◽  
Yoshiki Yoshida ◽  
...  
Keyword(s):  
Kinematic Analysis ◽  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Large Angle ◽  
Vertical Axis ◽  
Output Link ◽  
Analysis And Design ◽  
Revolute Joints ◽  
Full Rotation ◽  
Six Dof

The present paper proposes a new six-DOF parallel mechanism with three connecting chains. This mechanism can have a large angle of orientation of the output link. Joints in each connecting chain are arranged from the base in order of revolute, prismatic, spherical and revolute joints. All three revolute joints on the base are coaxial. With this structure, the output link can perform a full rotation around the vertical axis. The orientation capability of this mechanism is demonstrated. Equations for displacement analysis and the Jacobian matrix are derived. A design and prototype of this mechanism for a pipe-bender are shown.

Geometry and Kinematic Analysis of a Redundantly Actuated Parallel Mechanism That Eliminates Singularities and Improves Dexterity

2008 ◽  
Vol 130 (12) ◽  
Author(s):  
Jody A. Saglia ◽  
Jian S. Dai ◽  
Darwin G. Caldwell
Keyword(s):  
Condition Number ◽  
Kinematic Analysis ◽  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Parallel Mechanisms ◽  
Rank Deficiency ◽  
Actuation Redundancy ◽  
Ankle Rehabilitation ◽  
Redundantly Actuated ◽  
Lower Mobility

This paper investigates the behavior of a type of parallel mechanisms with a central strut. The mechanism is of lower mobility, redundantly actuated, and used for sprained ankle rehabilitation. Singularity and dexterity are investigated for this type of parallel mechanisms based on the Jacobian matrix in terms of rank deficiency and condition number, throughout the workspace. The nonredundant cases with three and two limbs are compared with the redundantly actuated case with three limbs. The analysis demonstrates the advantage of introducing the actuation redundancy to eliminate singularities and to improve dexterity and justifies the choice of the presented mechanism for ankle rehabilitation.

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