Configuration Workspaces of Series-Parallel Mechanisms

2012 ◽  
Author(s):  
Brian McCarthy ◽  
Mikola Lysenko ◽  
Vadim Shapiro
Keyword(s):  
Constraint Propagation ◽  
High Dimensionality ◽  
Topological Complexity ◽  
Parallel Mechanisms ◽  
End Effector ◽  
Manufacturing Process Planning ◽  
Design And Manufacturing ◽  
Lower Pair ◽  
Rigid Body Motions ◽  
New Formulation

The workspace of a mechanism is the set of positions and orientations that is reachable by its end effector. Workspaces have numerous applications, including motion planning, mechanism design, and manufacturing process planning, but their representation and computation is challenging due to high dimensionality and geometric/topological complexity. We propose a new formulation of the workspace computation problem for a large class of mechanisms represented by series-parallel constraint graphs. A wide variety of allowable constraints include all lower pair, some higher pair, and non-collision constraints. We show that the workspace of such mechanisms may be computed by a constraint propagation algorithm. After the space of all rigid body motions is discretized, these operations can be efficiently implemented using the Fast Fourier Transform and a depth first search. In contrast to algebraic formulations, the proposed method assures that all configurations in the computed workspace not only satisfy pairwise constraints but can be reached without breaking and reassembling the mechanism.

A Statically Balanced Gough/Stewart-Type Platform: Conception, Design, and Simulation

2009 ◽  
Vol 1 (3) ◽  
Author(s):  
Marco Carricato ◽  
Clément Gosselin
Keyword(s):  
Sufficient Conditions ◽  
Parallel Manipulators ◽  
Point Of View ◽  
Theoretical Point ◽  
Constant Force ◽  
Parallel Mechanisms ◽  
End Effector ◽  
Neutral Equilibrium ◽  
The Difference ◽  
Elastic Elements

Gravity compensation of spatial parallel manipulators is a relatively recent topic of investigation. Perfect balancing has been accomplished, so far, only for parallel mechanisms in which the weight of the moving platform is sustained by legs comprising purely rotational joints. Indeed, balancing of parallel mechanisms with translational actuators, which are among the most common ones, has been traditionally thought possible only by resorting to additional legs containing no prismatic joints between the base and the end-effector. This paper presents the conceptual and mechanical designs of a balanced Gough/Stewart-type manipulator, in which the weight of the platform is entirely sustained by the legs comprising the extensible jacks. By the integrated action of both elastic elements and counterweights, each leg is statically balanced and it generates, at its tip, a constant force contributing to maintaining the end-effector in equilibrium in any admissible configuration. If no elastic elements are used, the resulting manipulator is balanced with respect to the shaking force too. The performance of a study prototype is simulated via a model in both static and dynamic conditions, in order to prove the feasibility of the proposed design. The effects of imperfect balancing, due to the difference between the payload inertial characteristics and the theoretical/nominal ones, are investigated. Under a theoretical point of view, formal and novel derivations are provided of the necessary and sufficient conditions allowing (i) a body arbitrarily rotating in space to rest in neutral equilibrium under the action of general constant-force generators, (ii) a body pivoting about a universal joint and acted upon by a number of zero-free-length springs to exhibit constant potential energy, and (iii) a leg of a Gough/Stewart-type manipulator to operate as a constant-force generator.

Relevance and Transferability for Parallel Mechanisms With Reconfigurable Platforms

2019 ◽  
Vol 11 (3) ◽  
Author(s):  
Xi Kang ◽  
Jian S. Dai
Keyword(s):  
System Theory ◽  
Parallel Mechanism ◽  
Geometric Model ◽  
Parallel Mechanisms ◽  
End Effector ◽  
Kinematic Coupling ◽  
Reconfigurable Platforms ◽  
Reconfigurable Platform

The parallel mechanism with a reconfigurable platform retains all advantages of parallel mechanisms and provides additional functions by virtue of the reconfigurable platform, leading to kinematic coupling between limbs that restricts development of the mechanism. This paper aims at dealing with kinematic coupling between limbs by investigating the transferability of limb constraints and their degrees of relevance to the platform constraints based on the geometric model of the mechanism. The paper applies screw-system theory to verifying the degree of relevance between limb constraint wrenches and platform constraint wrenches, and reveals the transferability of limb constraints, to obtain the final resultant wrenches and twists of the end effector. The proposed method is extended to parallel mechanisms with planar n-bar reconfigurable platforms, spherical n-bar reconfigurable platforms, and other spatial reconfigurable platforms and lends itself to a way of studying a parallel mechanism with a reconfigurable platform.

Analyses of Error and Precision of 6-DOF Platform

2012 ◽  
Vol 591-593 ◽  
pp. 2081-2086 ◽  
Author(s):  
Rui Ren ◽  
Chang Chun Ye ◽  
Guo Bin Fan
Keyword(s):  
Inverse Kinematics ◽  
Newton Iteration ◽  
Forward Kinematics ◽  
Parallel Mechanisms ◽  
End Effector ◽  
C Programming Language ◽  
C Programming ◽  
Manufacturing Tolerances ◽  
Parallel Robotics ◽  
Forward Kinematic

A particular subset of 6-DOF parallel mechanisms is known as Stewart platforms (or hexapod). Stewart platform characteristic analyzed in this paper is the effect of small errors within its elements (strut lengths, joint placement) which can be caused by manufacturing tolerances or setting up errors or other even unknown sources to end effector. The biggest kinematics problem is parallel robotics which is the forward kinematics. On the basis of forward kinematic of 6-DOF platform, the algorithm model was built by Newton iteration, several computer programs were written in the MATLAB and Visual C++ programming language. The model is effective and real-time approved by forwards kinematics, inverse kinematics iteration and practical experiment. Analyzing the resource of error, get some related spectra map, top plat position and posture error corresponding every error resource respectively. By researching and comparing the error spectra map, some general results is concluded.

A Novel Origami Inspired Delta Mechanism with Flat Parallelogram Joints

2020 ◽  
pp. 1-22
Author(s):  
Merve Acer Kalafat ◽  
Hasan Sevinc ◽  
Shahrad Samankan ◽  
Atakan Altinkaynak ◽  
Zeynep Temel
Keyword(s):  
Design Methodology ◽  
Small Scale ◽  
Layer By Layer ◽  
Parallel Mechanisms ◽  
End Effector ◽  
High Speeds ◽  
Parallel Movement ◽  
Pick And Place ◽  
Kinematic Models ◽  
Kinematic Performance

Abstract In robotics, origami-based design methodology can be used to create small scale parallel mechanisms with easier assembly processes. Delta mechanisms are one of the famous parallel mechanism used mostly in pick and place operations due to their capability to reach high speeds and accelerations. In this work, we present a novel Delta mechanism fabricated with fully 2D layer by layer methods. In our design we have eliminated manual 3D processes in order to provide parallel movement of the links. We have designed a new flat parallelogram providing pure translations in X-Y-Z directions respecting to the conventional kinematic models for Delta mechanism. The assembly process is reduced to an only cut – laminate – repeat steps which are very basic operations in 2D. The kinematic performance of the mechanism has been analyzed using a 6 DoF position sensor placed on the end-effector. The mechanism has a 20x20x20 mm3 cubic stable workspace with a 17.5 mm radius circular footprint when it is completely flat. The tests were done for circular trajectories having 10 mm radius circles with different heights and circles with different radiuses in a specific height. Despite having no feedback control from the end effector, the mechanism was able to follow the trajectory with 1.5 mm RMS precision. We have also changed the materials of the flexible layers in passive links and presented the trajectory results of the end-effector showing how it effects the kinematic performance of the mechanism.

The Dimensional Synthesis of Spatial Cable-Driven Parallel Mechanisms

2013 ◽  
Vol 5 (4) ◽  
Author(s):  
K. Azizian ◽  
P. Cardou
Keyword(s):  
Synthesis Method ◽  
Sufficient Condition ◽  
Nonlinear Program ◽  
Parallel Mechanisms ◽  
Dimensional Synthesis ◽  
End Effector ◽  
A Value ◽  
Null Value ◽  
Objective Value

This paper presents a method for the dimensional synthesis of fully constrained spatial cable-driven parallel mechanisms (CDPMs), namely, the problem of finding a geometry whose wrench-closure workspace (WCW) contains a prescribed workspace. The proposed method is an extension to spatial CDPMs of a synthesis method previously published by the authors for planar CDPMs. The WCW of CDPMs is the set of poses for which any wrench can be produced at the end-effector by non-negative cable tensions. A sufficient condition is introduced in order to verify whether a given six-dimensional box, i.e., a box covering point-positions and orientations, is fully inside the WCW of a given spatial CDPM. Then, a nonlinear program is formulated, whose optima represent CDPMs that can reach any point in a set of boxes prescribed by the designer. The objective value of this nonlinear program indicates how well the WCW of the resulting CDPM covers the prescribed box, a null value indicating that none of the WCW is covered and a value greater or equal to one indicating that the full prescribed workspace is covered.

The Mechanics of Parallel Mechanisms and Walking Machines

1994 ◽  
Vol 208 (6) ◽  
pp. 367-377 ◽  
Author(s):  
S J Zhang ◽  
D J Sanger ◽  
D Howard
Keyword(s):  
Parallel Mechanism ◽  
Virtual Work ◽  
The Body ◽  
Position Vector ◽  
Parallel Mechanisms ◽  
Active Joint ◽  
End Effector ◽  
Walking Machine ◽  
Walking Machines ◽  
Fixed Base

A parallel mechanism is one whose links and joints form two or more serially connected chains which join the fixed base and the end effector The mechanism of a multi-legged walking machine can be considered as a parallel mechanism whose base is not fixed and whose configuration changes during different phases of its gait. This paper presents methods for analysing the mechanics of parallel mechanisms and walking machines using vector and screw algebra Firstly, displacement analysis is covered; this includes general methods for deriving the position vector of any joint in any leg and for calculating the active joint displacements in any leg. Secondly, velocity analysis is covered which tackles the problem of calculating active joint velocities given the velocity, position and the orientation of the body and the positions of the feet. Thirdly, the static analysis of these classes of mechanisms using the principle of virtual work and screw algebra is given. Expressions are derived for the actuator forces and torques required to balance a given end effector (or body) wrench and, in the case of a walking machine, the ground reactions at the feet. Numerical examples are given to demonstrate the application of these methods.

A Quasi-Static Model for Planar Compliant Parallel Mechanisms

2009 ◽  
Vol 1 (2) ◽  
Author(s):  
Cyril Quennouelle ◽  
Clément Gosselin
Keyword(s):  
Parallel Mechanism ◽  
Applied Load ◽  
Jacobian Matrix ◽  
Static Model ◽  
Parallel Mechanisms ◽  
Compliance Matrix ◽  
End Effector ◽  
Kinematic Constraints ◽  
Compliant Parallel Mechanism ◽  
External Loads

In this paper, the mobility, the kinematic constraints, the pose of the end-effector, and the static constraints that lead to the kinematostatic model of a compliant parallel mechanism are introduced. A formulation is then provided for its instantaneous variation—the quasi-static model. This new model allows the calculation of the variation in the pose as a linear function of the motion of the actuators and the variation in the external loads through two new matrices: the compliant Jacobian matrix and the Cartesian compliance matrix that give a simple and meaningful formulation of the model of the mechanism. Finally, a simple application to a planar four-bar mechanism is presented to illustrate the use of this model and the new possibilities that it opens, notably the study of the kinematics for any range of applied load.

scholarly journals Collision-free workspace of parallel mechanisms based on an interval analysis approach

Robotica ◽  
2016 ◽  
Vol 35 (8) ◽  
pp. 1747-1760 ◽  
Author(s):  
MohammadHadi FarzanehKaloorazi ◽  
Mehdi Tale Masouleh ◽  
Stéphane Caro
Keyword(s):  
Interval Analysis ◽  
Parallel Mechanism ◽  
Spherical Shape ◽  
Stewart Platform ◽  
Analysis Approach ◽  
Parallel Mechanisms ◽  
Planar Case ◽  
End Effector ◽  
Mechanical Interference

SUMMARYThis paper proposes an interval-based approach in order to obtain the obstacle-free workspace of parallel mechanisms containing one prismatic actuated joint per limb, which connects the base to the end-effector. This approach is represented through two cases studies, namely a 3-RPR planar parallel mechanism and the so-called 6-DOF Gough–Stewart platform. Three main features of the obstacle-free workspace are taken into account: mechanical stroke of actuators, collision between limbs and obstacles and limb interference. In this paper, a circle(planar case)/spherical(spatial case) shaped obstacle is considered and its mechanical interference with limbs and edges of the end-effector is analyzed. It should be noted that considering a circle/spherical shape would not degrade the generality of the problem, since any kind of obstacle could be replaced by its circumscribed circle/sphere. Two illustrative examples are given to highlight the contributions of the paper.

Process Planning in Manufacturing Systems

2015 ◽  
Vol 760 ◽  
pp. 745-750
Author(s):  
Cristian Tarba ◽  
Sergiu Tonoiu ◽  
Petre Gheorghe Tiriplica ◽  
Ionut Gabriel Ghionea
Keyword(s):  
Product Design ◽  
Process Planning ◽  
Manufacturing Process ◽  
Manufacturing Systems ◽  
Planning Process ◽  
Physical Entity ◽  
Manufacturing Process Planning ◽  
Design And Manufacturing

The process of the product design consists in a plan for the product, its components and subassemblies. To obtain the physical entity building a manufacturing plan is needed. The activity of developing such a manufacturing plan is name process planning. Process planning is the relation between design and manufacturing. Process planning consists in defining the sequence of the steps that should be taken to make the product. Process planning is referring to the engineering and technological issues of how to make it.

Design and Control of Planar Parallel Mechanisms with High Speed and High Precision

2006 ◽  
Vol 315-316 ◽  
pp. 872-0
Author(s):  
L.N. Sun ◽  
Y.J. Liu ◽  
J. Li ◽  
J. Cui
Keyword(s):  
High Precision ◽  
Disturbance Observer ◽  
High Speed ◽  
Optimization Design ◽  
Advanced Manufacturing ◽  
Parallel Mechanisms ◽  
Direct Drive ◽  
End Effector ◽  
Load Disturbance ◽  
And Control

In order to satisfy the requirement of advanced manufacturing equipments with high speed and high precision, two planar parallel mechanisms have been developed. Based on these mechanisms, firstly, in consideration with the velocity and the precision of the end-effector together, the dimension optimization design is performed based on conditioning index and the precision characteristics. Then a disturbance observer is designed for the purpose of restraining load disturbance in the direct-drive system, and the experimental results show that load disturbance can be effectively restrained by the disturbance observer.

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