Singularity analysis of two-legged planar parallel robots with three degrees of freedom

2016 ◽  
Vol 232 (4) ◽  
pp. 657-664 ◽  
Author(s):  
Mustafa Özdemir
Keyword(s):  
Degrees Of Freedom ◽  
Singularity Analysis ◽  
Parallel Robots ◽  
Design Concept ◽  
Type I ◽  
Numerical Examples ◽  
Three Degrees Of Freedom

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.

Dynamic Point-To-Point Trajectory Planning for Three Degrees-of-Freedom Cable-Suspended Parallel Robots Using Rapidly Exploring Random Tree Search

2020 ◽  
Vol 12 (4) ◽  
Author(s):  
Sheng Xiang ◽  
Haibo Gao ◽  
Zhen Liu ◽  
Clément Gosselin
Keyword(s):  
Trajectory Planning ◽  
Degrees Of Freedom ◽  
Parallel Robots ◽  
Tree Search ◽  
Planning Techniques ◽  
Motion Primitive ◽  
Planning Technique ◽  
Point To Point ◽  
Three Degrees Of Freedom ◽  
Specific Distance

Abstract This paper proposes a dynamic point-to-point trajectory planning technique for three degrees-of-freedom (DOFs) cable-suspended parallel robots. The proposed technique is capable of generating feasible multiple-swing trajectories that reach points beyond the footprint of the robot. Tree search algorithms are used to automatically determine a sequence of intermediate points to enhance the versatility of the planning technique. To increase the efficiency of the tree search, a one-swing motion primitive and a steering motion primitive are designed based on the dynamic model of the robot. Closed-form expressions for the motion primitives are given, and a corresponding rapid feasibility check process is proposed. An energy-based metric is used to estimate the distance in the Cartesian space between two points of a dynamic point-to-point task, and this system’s specific distance metric speeds up the coverage. The proposed technique is evaluated using a series of Monte Carlo runs, and comparative statistics results are given. Several example trajectories are presented to illustrate the approach. The results are compared with those obtained with the existing state-of-the-art methods, and the proposed technique is shown to be more general compared to previous analytical planning techniques while generating smoother trajectories than traditional rapidly exploring randomized tree (RRT) methods.

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.

Performing Nonsingular Transitions Between Assembly Modes in Analytic Parallel Manipulators by Enclosing Quadruple Solutions

2015 ◽  
Vol 137 (12) ◽  
Author(s):  
Adrián Peidró ◽  
José María Marín ◽  
Arturo Gil ◽  
Óscar Reinoso
Keyword(s):  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
Joint Space ◽  
Parallel Robots ◽  
Forward Kinematics ◽  
Characteristic Polynomials ◽  
Forward Kinematic ◽  
Three Degrees Of Freedom

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.

scholarly journals Technology-Oriented Optimization of the Secondary Design Parameters of Robots for High-Speed Machining Applications

2010 ◽  
Author(s):  
Se´bastien Briot ◽  
Anatol Pashkevich ◽  
Damien Chablat
Keyword(s):  
Machine Tools ◽  
High Speed ◽  
Degrees Of Freedom ◽  
Parallel Robots ◽  
Design Parameters ◽  
Speed Up ◽  
Parallel Kinematic ◽  
Parallel Kinematic Machine Tools ◽  
Accuracy Constraints ◽  
Three Degrees Of Freedom

In this paper, a new methodology for the optimal design of the secondary geometric parameters (shape of links, size of the platform, etc.) of parallel kinematic machine tools is proposed. This approach aims at minimizing the total mass of the robot under position accuracy constraints. This methodology is applied to two translational parallel robots with three degrees-of-freedom (DOF): the Y-STAR and the UraneSX. The proposed approach is able to speed up the design process and to help the designer to find more quickly a set of design parameters.

scholarly journals Kinematics, Workspace, and Singularity Analysis of a Parallel Robot With Five Operation Modes

2018 ◽  
Vol 10 (3) ◽  
Author(s):  
Damien Chablat ◽  
Xianwen Kong ◽  
Chengwei Zhang
Keyword(s):  
Degrees Of Freedom ◽  
Rotation Axis ◽  
Operation Mode ◽  
Parallel Robot ◽  
Joint Space ◽  
Singularity Analysis ◽  
Parallel Robots ◽  
Operation Modes ◽  
Serial Chain ◽  
Kinematic Study

Most multimode parallel robots can change operation modes by passing through constraint singularities. This paper deals with a comprehensive kinematic study of a three degrees-of-freedom (DOF) multimode three-PRPiR parallel robot developed at Heriot-watt University. This robot is able to reach several operation modes without crossing any constraint singularity by using lockable Pi and R joints. Here, a Pi joint may act as a 1DOF planar parallelogram if its lockable P (prismatic) joint is locked or a 2DOF RR serial chain if its lockable P joint is released. The operation modes of the robot include a 3T operation mode and four 2T1R operation modes with two different directions of the rotation axis of the moving platform. The inverse kinematics and forward kinematics of the robot in each operation mode are dealt with in detail. The joint space and workspace analysis of the robot allow us to know the regions of the workspace that the robot can reach in each operation mode. It is shown that the robot is able to change assembly mode in one operation mode by passing through another operation mode.

Numerical Framework and Design Optimization of an Intrinsically Compliant 3-DOF Parallel Robot

2020 ◽  
Vol 21 (2) ◽  
Author(s):  
Shahid Hussain ◽  
Prashant K. Jamwal ◽  
Akim Kapsalyamov ◽  
Mergen H. Ghayesh
Keyword(s):  
Degrees Of Freedom ◽  
Parallel Robot ◽  
Singularity Analysis ◽  
Parallel Robots ◽  
Simultaneous Optimization ◽  
Design Synthesis ◽  
Pneumatic Muscle ◽  
Nonlinear Motion ◽  
Strength Pareto Evolutionary Algorithm ◽  
Muscle Actuators

Abstract Parallel robots are multiple degrees of freedom (DOFs) systems that are typically used in applications characterized by enhanced accuracy, rigidity, and large force requirements within a compact workspace. In the present research, an intrinsically compliant parallel robot with 3-DOFs, actuated using four pneumatic muscle actuators (PMA), is conceptualized, developed, and analyzed. Despite many benefits, parallel robots also offer certain challenges that arise from the highly coupled and nonlinear motion of their actuators. The small workspace of parallel robots has many singularities and solving a closed-form forward kinematics (FK) for its end-effector motion is complicated. The PMAs can provide intrinsically compliant robotic motions, however, since they are flexible, their unilateral actuation also poses constraints on the achievable DOFs. The present research focuses on analyzing kinematics and dynamics of the developed parallel robot incorporating the stiffness together with force closure analyses besides suggesting design improvements as a consequence of the singularity analysis. Design synthesis and multi-criteria optimization have been performed to obtain a robot design which may provide higher accuracies (near unity condition number), quick response to external wrench (stiffness and rigidity), and reduced actuator force requirements. SPEA2 (Improved Strength Pareto Evolutionary Algorithm) has been implemented to carry out the simultaneous optimization of design objectives and provide Pareto optimal design solutions.

Topological and Geometrical Synthesis of Three-Degree-of-Freedom Fully Parallel Manipulators by Instantaneous Kinematics

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Xiaoyu Wang ◽  
Luc Baron ◽  
Guy Cloutier
Keyword(s):  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
Synthesis Process ◽  
End Effector ◽  
Numerical Examples ◽  
Passive Joint ◽  
New Synthesis ◽  
Synthesis Procedure ◽  
Three Degree Of Freedom ◽  
Three Degrees Of Freedom

This paper presents a new synthesis procedure of fully parallel manipulators (PMs) of three degrees of freedom (DOFs) that could be implemented in a computer-aided synthesis process. Possible designs of PMs are represented by a set of unit joint twists at an initial configuration, called here topological and geometric parameters (TGPs). This makes it possible to represent PMs of all topologies and geometries in an easy and consistent way. The kinematic bond between the end effector (EE) and the base is then formulated as a set of equations involving TGPs, actuated-joint variables, and non-actuated-joint variables (passive joints). To achieve the required type of EE motion, possible topologies are first derived from tangent space analysis, and then the feasible topologies are retained by further displacement analysis. The geometries are determined such that the set of equations should be isoconstrained when passive-joint variables are taken as unknowns. The synthesis procedure of 3DOF PMs is illustrated with three numerical examples: one producing a new architecture of one translation and two rotations, while the other two producing existing architectures of translational PMs.

scholarly journals Modeling and Control of a Cable-Suspended Sling-Like Parallel Robot for Throwing Operations

2020 ◽  
Vol 10 (24) ◽  
pp. 9067
Author(s):  
Deng Lin ◽  
Giovanni Mottola ◽  
Marco Carricato ◽  
Xiaoling Jiang
Keyword(s):  
Mathematical Models ◽  
Degrees Of Freedom ◽  
Parallel Robot ◽  
Parallel Robots ◽  
Target Point ◽  
Inertial Effects ◽  
End Effector ◽  
Modeling And Control ◽  
And Control ◽  
Three Degrees Of Freedom

Cable-driven parallel robots can provide interesting advantages over conventional robots with rigid links; in particular, robots with a cable-suspended architecture can have very large workspaces. Recent research has shown that dynamic trajectories allow the robot to further increase its workspace by taking advantage of inertial effects. In our work, we consider a three-degrees-of-freedom parallel robot suspended by three cables, with a point-mass end-effector. This model was considered in previous works to analyze the conditions for dynamical feasibility of a trajectory. Here, we enhance the robot’s capabilities by using it as a sling, that is, by throwing a mass at a suitable time. The mass is carried at the end-effector by a gripper, which releases the mass so that it can reach a given target point. Mathematical models are presented that provide guidelines for planning the trajectory. Moreover, results are shown from simulations that include the effect of cable elasticity. Finally, suggestions are offered regarding how such a trajectory can be optimized.

scholarly journals Rotational Workspace Expansion of a Planar CDPR with a Circular End-Effector Mechanism Allowing Passive Reconfiguration

Robotics ◽  
2019 ◽  
Vol 8 (3) ◽  
pp. 57 ◽  
Author(s):  
Marco Carpio Alemán ◽  
Roque Saltaren ◽  
Alejandro Rodriguez ◽  
Gerardo Portilla ◽  
Juan Placencia
Keyword(s):  
Degrees Of Freedom ◽  
Parallel Robot ◽  
Parallel Robots ◽  
End Effector ◽  
Effector Mechanism ◽  
Circular Structure ◽  
Adams Software ◽  
Anchor Points ◽  
Orientation Workspace ◽  
Three Degrees Of Freedom

Cable-Driven Parallel Robots (CDPR) operate over a large positional workspace and a relatively large orientation workspace. In the present work, the expansion of the orientation Wrench Feasible Workspace (WFW) in a planar four-cable passive reconfigurable parallel robot with three degrees of freedom was determined. To this end, we proposed a circular-geometry effector mechanism, whose structure allows automatic mobility of the two anchor points of the cables supporting the End Effector (EE). The WFW of the proposed circular structure robot was compared with that of a traditional robot with a rectangular geometry and fixed anchor points. Considering the feasible geometric and tension forces on the cables, the generated workspace volume of the robot was demonstrated in an analysis-by-intervals. The results were validated by simulating the orientation movements of the robot in ADAMS software and a real experimental test was developed for a hypothetical case. The proposed design significantly expanded the orientation workspace of the robot. The remaining limitation is the segment of the travel space in which the mobile connection points can slide. Overcoming this limitation would enable the maximum rotation of the EE.

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