A Class of Fully Parallel Manipulators with Closed-Form Forward Position Kinematics

1996 ◽  
pp. 411-420 ◽  
Author(s):  
Herman Bruyninckx ◽  
Joris De Schutter
Keyword(s):  
Closed Form ◽  
Parallel Manipulators

Workspaces of Cable-Actuated Parallel Manipulators

2005 ◽  
Vol 128 (1) ◽  
pp. 159-167 ◽  
Author(s):  
Ethan Stump ◽  
Vijay Kumar
Keyword(s):  
Closed Form ◽  
Linear Algebra ◽  
Convex Analysis ◽  
Analytical Techniques ◽  
Parallel Manipulators ◽  
Parallel Mechanisms ◽  
Cable Forces

This paper develops analytical techniques to delineate the workspace boundaries for parallel mechanisms with cables. In such mechanisms, it is not only necessary to solve the closure equations but it is also essential to verify that equilibrium can be achieved with non-negative actuator (cable) forces. We use tools from convex analysis and linear algebra to derive closed-form expressions for the workspace boundaries and illustrate the applications using planar and spatial examples.

Workspace Analysis and Going through Singularities of 5-Bar Symmetric Planar Parallel Manipulator by Automated Selective Actuation Mechanism

2012 ◽  
Vol 588-589 ◽  
pp. 1664-1668
Author(s):  
Syam Sundar ◽  
Vijay S. Rathore ◽  
Manoj K. Sahi ◽  
V. Upendran ◽  
Anjan Kumar Dash
Keyword(s):  
Closed Form ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
New Approach ◽  
Serial Manipulators ◽  
Actuation Mechanism ◽  
Geometric Conditions ◽  
Workspace Analysis ◽  
Planar Parallel Manipulator ◽  
Planar Parallel Manipulators

In this article‚ a new approach is presented to determine the various shapes of workspaces of 5 bar symmetric planar parallel manipulators. Here the shape of the workspace is determined by the number of ways the workspaces of the two serial manipulators intersect with each other. Geometric conditions are established in each case and area of each shape of workspace is determined in closed form. Singularity is another important consideration in the design of parallel manipulators. In this paper, an approach is presented to go through the singularity points using an automatic selective actuation mechanism. A prototype 5-bar planar manipulator is fabricated along with an automatic selective actuation mechanism demonstrating the manipulator going through the singularity points.

Geometry and Position Analysis of a Novel Class of Hybrid Manipulators

1994 ◽  
Author(s):  
Change-de Zhang ◽  
Shin-Min Song
Keyword(s):  
Closed Form ◽  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
Parallel Mechanisms ◽  
Serial Manipulators ◽  
Closed Form Solutions ◽  
Position Analysis ◽  
Hybrid Manipulator ◽  
Load Carrying ◽  
Inverse Position Analysis

Abstract This paper presents a novel class of hybrid manipulators composed of two serially connected parallel mechanisms, each of which has three degrees of freedom. The lower and upper platforms respectively control the position and orientation of the end-effector. The advantages of this type of hybrid manipulator are larger workspace (as compared with parallel manipulators) and better rigidity and higher load-carrying capability (as compared with serial manipulators). The closed-form solutions of the forward and inverse position analyses are discussed. For forward position analysis, it is shown that the resultant equation for the positional mechanism is an 8-th order, a 6-th order, a 4-th order, or a 2-nd order polynomial, depending on the geometry and joint types of the passive subchain, while for the orientational mechanism, it is an 8-th order, or a 2-nd polynomial depending on the geometry. For inverse position analysis, it is demonstrated that the positional and orientational mechanisms both possess analytical closed-form solutions.

New Resolution Scheme of the Forward Kinematics of Parallel Manipulators Using Extra Sensors

1996 ◽  
Vol 118 (2) ◽  
pp. 214-219 ◽  
Author(s):  
Kilryong Han ◽  
Wankyun Chung ◽  
Y. Youm
Keyword(s):  
Closed Form ◽  
Real Time ◽  
Parallel Manipulators ◽  
Stewart Platform ◽  
Forward Kinematics ◽  
Numerical Examples ◽  
Resolution Scheme ◽  
Real Time Applications ◽  
Forward Kinematic Problem ◽  
Forward Kinematic

This paper presents a new closed-form resolution scheme of the forward kinematics of parallel manipulators based on two concepts, local structurization and mechanism partition. This scheme is applied to 6-DOF Stewart platform manipulators and the effectiveness of this scheme is verified through numerical examples. It is shown that one extra sensor is sufficient for both 3-3 SPM and 6-3 SPM to exactly resolve the forward kinematic problem (FKP) in closed form and two sensors for 6-6 SPM. In previous research, at least three extra sensors were needed for closed-form resolution of the FKP for 6-6 SPM. Consequently, the new resolution scheme is efficient to implement and easy for real-time applications for the control of parallel manipulators.

Closed form solution to the position workspace of Stewart parallel manipulators

1998 ◽  
Vol 41 (4) ◽  
pp. 393-403 ◽  
Author(s):  
Tian Huang ◽  
Jinsong Wang ◽  
D. J. Whitehouse
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Parallel Manipulators ◽  
Form Solution

Determination of the closed-form workspace area expression and dimensional optimization of planar parallel manipulators

Robotica ◽  
2016 ◽  
Vol 35 (10) ◽  
pp. 2056-2075 ◽  
Author(s):  
M. Ganesh ◽  
Banke Bihari ◽  
Vijay Singh Rathore ◽  
Dhiraj Kumar ◽  
Chandan Kumar ◽  
...  
Keyword(s):  
Closed Form ◽  
Degrees Of Freedom ◽  
Solution Space ◽  
Optimization Procedure ◽  
Parallel Manipulators ◽  
Force Transmission ◽  
Workspace Analysis ◽  
Planar Parallel Manipulator ◽  
Transmission Index ◽  
Planar Parallel Manipulators

SUMMARYOptimization is an important step in the design and development of a planar parallel manipulator. For optimization processes, workspace analysis is a crucial and preliminary objective. Generally, the workspace analysis for such manipulators is carried out using a non-dimensional approach. For planar parallel manipulators of two degrees of freedom (2-DOF), a non-dimensional workspace analysis is very advantageous. However, it becomes very difficult in the case of 3-DOF and higher DOF manipulators because of the complex shape of the workspace. In this study, the workspace shape is classified as a function of the geometric parameters, and the closed-form area expressions are derived for a constant orientation workspace of a three revolute–revolute–revolute (3-RRR) planar manipulator. The approach is also shown to be feasible for different orientations of a mobile platform. An optimization procedure for the design of planar 3-RRR manipulators is proposed for a prescribed workspace area. It is observed that the closed-form area expression for all the possible shapes of the workspace provides a larger solution space, which is further optimized considering singularity, mass of the manipulator, and a force transmission index.

Forward and Inverse Displacement Analysis of a Novel Three-Legged Mobile Robot Based on the Kinematics of In-Parallel Manipulators

2007 ◽  
Author(s):  
Ping Ren ◽  
Ivette Morazzani ◽  
Dennis Hong
Keyword(s):  
Mobile Robot ◽  
Closed Form ◽  
Joint Angle ◽  
Parallel Manipulators ◽  
Geometric Constraints ◽  
Walking Robot ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Closed Form Solutions ◽  
Displacement Information

This paper presents the forward and inverse displacement analysis of a novel three-legged walking robot STriDER (Self-excited Tripedal Dynamic Experimental Robot). STriDER utilizes the concept of passive dynamic locomotion to walk, but when all three feet of the robot are on the ground, the kinematic structure of the robot behaves like an in-parallel manipulator. To plan and control its change of posture, the kinematics of its forward and inverse displacement must be analyzed. First, the concept of this novel walking robot and its unique tripedal gait is discussed including strategies for changing directions, followed by the overall kinematic configuration and definitions of its coordinate frames. When all three feet of the robot are on the ground, by assuming there are no slipping at the feet, each foot contact point are treated as a spherical joint. Kinematic analysis methods for in-parallel manipulators are briefly reviewed and adopted for the forward and inverse displacement analysis for this mobile robot. Both loop-closure equations based on geometric constraints and the intersection of the loci of the feet are utilized to solve the forward displacement problem. Closed-form solutions are identified and discussed in the cases of redundant sensing with displacement information from nine, eight and seven joint angle sensors. For the non redundant sensing case using information from six joint angle sensors, it is shown that closed-form solutions can only be obtained when the displacement information is available from non-equally distributed joint angle sensors among the three legs. As for the case when joint angle sensors are equally distributed among the three legs, it will result in a 16th-order polynomial of a single variable. Finally, results from the simulations are presented for both inverse displacement analysis and the non redundant sensing case with equally distributed joint angle sensors. It was found that at most sixteen forward displacement solutions exist if displacement information from two joint angle sensors per leg are used and one is not used.

LAGRANGIAN DYNAMICS OF CABLE-DRIVEN PARALLEL MANIPULATORS: A VARIABLE MASS FORMULATION

2011 ◽  
Vol 35 (4) ◽  
pp. 529-542 ◽  
Author(s):  
Yousef B. Bedoustani ◽  
Pascal Bigras ◽  
Hamid D. Taghirad ◽  
Ilian A. Bonev
Keyword(s):  
Robust Control ◽  
Closed Form ◽  
Variable Mass ◽  
Parallel Manipulators ◽  
Complete Analysis ◽  
Control Synthesis ◽  
Mass Treatment ◽  
Lagrangian Dynamics ◽  
Lagrangian Variable ◽  
Inertial Parameters

In this paper, dynamic analysis of cable-driven parallel manipulators (CDPMs) is performed using the Lagrangian variable mass formulation. This formulation is used to treat the effect of a mass stream entering into the system caused by elongation of the cables. In this way, a complete dynamic model of the system is derived, while preserving the compact and tractable closed-form dynamics formulation. First, a general formulation for a CDPM is given, and the effect of change of mass in the cables is integrated into its dynamics. The significance of such a treatment is that a complete analysis of the dynamics of the system is achieved, including vibrations, stability, and any robust control synthesis of the manipulator. The formulation obtained is applied to a typical planar CDPM. Through numerical simulations, the validity and integrity of the formulations are verified, and the significance of the variable mass treatment in the analysis is examined. For this example, it is shown that the effect of introducing a mass stream into the system is not negligible. Moreover, it is non linear and strongly dependent on the geometric and inertial parameters of the robot, as well as the maneuvering trajectory.

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