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

Author(s):  
Grigore Gogu

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.

Author(s):  
Grigore Gogu

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.


Robotica ◽  
2009 ◽  
Vol 27 (1) ◽  
pp. 79-101 ◽  
Author(s):  
G. Gogu

SUMMARYThe paper presents structural synthesis of maximally regular T3R2-type parallel robotic manipulators (PMs) with five degrees of freedom. The moving platform has three independent translations (T3) and two rotations (R2). A method is proposed for structural synthesis of maximally regular T3R2-type PMs based on the theory of linear transformations and evolutionary morphology. 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 maximally regular T3R2-type PMs presented in this paper is the 5×5 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. Kinematic analysis of maximally regular parallel robots is trivial and no computation is required for real-time control. This paper presents in a unified approach the structural synthesis of PMs with five degrees of freedom with decoupled and uncoupled motions, along with the maximally regular solutions.


2015 ◽  
Vol 137 (12) ◽  
Author(s):  
Adrián Peidró ◽  
José María Marín ◽  
Arturo Gil ◽  
Óscar Reinoso

This paper analyzes the multiplicity of the solutions to forward kinematics of two classes of analytic robots: 2RPR-PR robots with a passive leg and 3-RPR robots with nonsimilar flat platform and base. Since their characteristic polynomials cannot have more than two valid roots, one may think that triple solutions, and hence nonsingular transitions between different assembly modes, are impossible for them. However, the authors show that the forward kinematic problems of these robots always admit quadruple solutions and obtain analytically the loci of points of the joint space where these solutions occur. Then, it is shown that performing trajectories in the joint space that enclose these points can produce nonsingular transitions, demonstrating that it is possible to design simple analytic parallel robots with two and three degrees-of-freedom (DOF) and the ability to execute these transitions.


Author(s):  
R. Jha ◽  
D. Chablat ◽  
F. Rouillier ◽  
G. Moroz

Trajectory planning is a critical step while programming the parallel manipulators in a robotic cell. The main problem arises when there exists a singular configuration between the two poses of the end-effectors while discretizing the path with a classical approach. This paper presents an algebraic method to check the feasibility of any given trajectories in the workspace. The solutions of the polynomial equations associated with the trajectories are projected in the joint space using Gröbner based elimination methods and the remaining equations are expressed in a parametric form where the articular variables are functions of time t unlike any numerical or discretization method. These formal computations allow to write the Jacobian of the manipulator as a function of time and to check if its determinant can vanish between two poses. Another benefit of this approach is to use a largest workspace with a more complex shape than a cube, cylinder or sphere. For the Orthoglide, a three degrees of freedom parallel robot, three different trajectories are used to illustrate this method.


2021 ◽  
Author(s):  
Amin Moosavian

The ability to vary the geometry of a wing to adapt to different flight conditions can significantly improve the performance of an aircraft. However, the realization of any morphing concept will typically be accompanied by major challenges. Specifically, the geometrical constraints that are imposed by the shape of the wing and the magnitude of the air and inertia loads make the usage of conventional mechanisms inefficient for morphing applications. Such restrictions have served as inspirations for the design of a modular morphing concept, referred to as the Variable Geometry Wing-box (VGW). The design for the VGW is based on a novel class of reconfigurable robots referred to as Parallel Robots with Enhanced Stiffness (PRES) which are presented in this dissertation. The underlying feature of these robots is the efficient exploitation of redundancies in parallel manipulators. There have been three categories identified in the literature to classify redundancies in parallel manipulators: 1) actuation redundancy, 2) kinematic redundancy, and 3) sensor redundancy. A fourth category is introduced here, referred to as 4) static redundancy. The latter entails several advantages traditionally associated only with actuation redundancy, most significant of which is enhanced stiffness and static characteristics, without any form of actuation redundancy. Additionally, the PRES uses the available redundancies to 1) control more Degrees of Freedom (DOFs) than there are actuators in the system, that is, under-actuate, and 2) provide multiple degrees of fault tolerance. Although the majority of the presented work has been tailored to accommodate the VGW, it can be applied to any comparable system, where enhanced stiffness or static characteristics may be desired without actuation redundancy. In addition to the kinematic and the kinetostatic analyses of the PRES, which are developed and presented in this dissertation along with several case-studies, an optimal motion control algorithm for minimum energy actuation is proposed. Furthermore, the optimal configuration design for the VGW is studied. The optimal configuration design problem is posed in two parts: 1) the optimal limb configuration, and 2) the optimal topological configuration. The former seeks the optimal design of the kinematic joints and links, while the latter seeks the minimal compliance solution to their placement within the design space. In addition to the static and kinematic criteria required for reconfigurability, practical design considerations such as fail-safe requirements and design for minimal aeroelastic impact have been included as constraints in the optimization process. The effectiveness of the proposed design, analysis, and optimization is demonstrated through simulation and a multi-module reconfigurable prototype.


Author(s):  
J. A. Carretero ◽  
R. P. Podhorodeski ◽  
M. Nahon

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.


Author(s):  
Richard Stamper ◽  
Lung-Wen Tsai

Abstract The dynamics of a parallel manipulator with three translational degrees of freedom are considered. Two models are developed to characterize the dynamics of the manipulator. The first is a traditional Lagrangian based model, and is presented to provide a basis of comparison for the second approach. The second model is based on a simplified Newton-Euler formulation. This method takes advantage of the kinematic structure of this type of parallel manipulator that allows the actuators to be mounted directly on the base. Accordingly, the dynamics of the manipulator is dominated by the mass of the moving platform, end-effector, and payload rather than the mass of the actuators. This paper suggests a new method to approach the dynamics of parallel manipulators that takes advantage of this characteristic. Using this method the forces that define the motion of moving platform are mapped to the actuators using the Jacobian matrix, allowing a simplified Newton-Euler approach to be applied. This second method offers the advantage of characterizing the dynamics of the manipulator nearly as well as the Lagrangian approach while being less computationally intensive. A numerical example is presented to illustrate the close agreement between the two models.


2015 ◽  
Vol 8 (2) ◽  
Author(s):  
Jun Wu ◽  
Binbin Zhang ◽  
Liping Wang

The paper deals with the evaluation of acceleration of redundant and nonredundant parallel manipulators. The dynamic model of three degrees-of-freedom (3DOF) parallel manipulator is derived by using the virtual work principle. Based on the dynamic model, a measure is proposed for the acceleration evaluation of the redundant parallel manipulator and its nonredundant counterpart. The measure is designed on the basis of the maximum acceleration of the mobile platform when one actuated joint force is unit and other actuated joint forces are less than or equal to a unit force. The measure for evaluation of acceleration can be used to evaluate the acceleration of both redundant parallel manipulators and nonredundant parallel manipulators. Furthermore, the acceleration of the 4-PSS-PU parallel manipulator and its nonredundant counterpart are compared.


Author(s):  
Mustafa Özdemir

Planar two-legged parallel robots with three degrees of freedom have been suggested in the literature as a solution to reduce the leg interference problem of their conventional three-legged counterparts, and since then have attracted considerable attention. This paper presents a singularity analysis of these robots. Three alternatives, namely the robots with 2-RRR, 2-RPR, and 2-PRR structures are considered. Type I, II, and III singularity conditions are obtained taking into account all possible actuation schemes. Several singularity-free actuation schemes are enumerated and discussed. The performed analysis also shows that adjustable designs are possible for manipulators with 2-PRR structures to have singularity-free operation. The proposed design concept and its effectiveness are illustrated through numerical examples.


2005 ◽  
Vol 291-292 ◽  
pp. 495-500
Author(s):  
Ping Zou

In this paper, the moving platform of the biglide parallel grinder with six degrees of freedom will keep moving horizontally at any time using parallelograms. Besides grinding the helical drill point, this grinder also can work as drilling and welding machine tool as well as a CMM. The joint-velocity Jacobian matrix is calculated. Moreover, the dynamic equations are derived by applying the Lagrangian formulation.


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