Determination of Singularity-Free Zones in the Workspace of Planar Parallel Mechanisms with Revolute Actuators

2011 ◽  
Vol 121-126 ◽  
pp. 1992-1996 ◽  
Author(s):  
Shu Jun Li ◽  
Clément Gosselin
Keyword(s):  
Trajectory Planning ◽  
Parallel Mechanism ◽  
Numerical Results ◽  
Parallel Mechanisms ◽  
Kinematic Design ◽  
Cartesian Space ◽  
Singularity Locus

The singularity-free workspace of parallel mechanisms is important in the trajectory planning and the kinematic design of the mechanisms. The planar parallel mechanism with revolute actuators, which the expression for the singularity locus and the algorithms for determining the singularity-free zones involve both the Cartesian and the joint variables, has been studied in the paper. Algorithms are proposed here to simplify the determination of the singularity-free zones in Cartesian space. The methodology and procedures for determining the singularity-free zones of planar parallel mechanisms with revolute actuators are introduced. The numerical results show that the simplified algorithms and the techniques are correct and efficient in determining singularity-free zones in the workspace of planar parallel mechanisms.

Determination of the Singularity Loci of Spherical Three-Degree-of-Freedom Parallel Manipularors

1992 ◽  
Author(s):  
Clément M. Gosselin ◽  
Jaouad Sefrioui
Keyword(s):  
Graphical Representation ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
End Effector ◽  
Cartesian Space ◽  
Singularity Locus ◽  
Three Degree Of Freedom ◽  
Analytical Expressions

Abstract In this paper, an algorithm for the determination of the singularity loci of spherical three-degree-of-freedom parallel manipulators with prismatic atuators is presented. These singularity loci, which are obtained as curves or surfaces in the Cartesian space, are of great interest in the context of kinematic design. Indeed, it has been shown elsewhere that parallel manipulators lead to a special type of singularity which is located inside the Cartesian workspace and for which the end-effector becomes uncontrollable. It is therfore important to be able to identify the configurations associated with theses singularities. The algorithm presented is based on analytical expressions of the determinant of a Jacobian matrix, a quantity that is known to vanish in the singular configurations. A general spherical three-degree-of-freedom parallel manipulator with prismatic actuators is first studied. Then, several particular designs are investigated. For each case, an analytical expression of the singularity locus is derived. A graphical representation in the Cartesian space is then obtained.

A 3-ṞPR Parallel Mechanism With Singularities That are Self-Motions

2010 ◽  
Vol 2 (3) ◽  
Author(s):  
Novona Rakotomanga ◽  
Ilian A. Bonev
Keyword(s):  
Parallel Mechanism ◽  
Control Strategies ◽  
Joint Space ◽  
Degree Of Freedom ◽  
Parallel Mechanisms ◽  
Active Joint ◽  
Cartesian Space ◽  
Three Degree Of Freedom

The Cartesian workspace of most three-degree-of-freedom parallel mechanisms is divided by Type 2 (also called parallel) singularity surfaces into several regions. Accessing more than one such region requires crossing a Type 2 singularity, which is risky and calls for sophisticated control strategies. Some mechanisms can still cross these Type 2 singularity surfaces through “holes” that represent Type 1 (also called serial) singularities only. However, what is even more desirable is if these Type 2 singularity surfaces were curves instead. Indeed, there exists at least one such parallel mechanism (the agile eye) and all of its singularities are self-motions. This paper presents another parallel mechanism, a planar one, whose singularities are self-motions. The singularities of this novel mechanism are studied in detail. While the Type 2 singularities in the Cartesian space still constitute a surface, they degenerate into lines in the active-joint space, which is the main result of this paper.

Kinematic Analysis and Singularity Representation of 5-RPRRR Parallel Mechanisms

2007 ◽  
Author(s):  
Mehdi Tale Masouleh ◽  
Cle´ment Gosselin
Keyword(s):  
Algebraic Geometry ◽  
Parallel Mechanism ◽  
Inverse Kinematic ◽  
Parallel Mechanisms ◽  
Inverse Kinematic Problem ◽  
Kinematic Geometry ◽  
Kinematic Properties ◽  
Orientation Workspace ◽  
Principal Contribution

This paper presents a novel type of five-degree-of-freedom parallel mechanism generating the 3T2R motion with linear inputs. The kinematic geometry of the mechanism is presented and several important kinematic issues including the inverse kinematic problem, the vector-loop velocity equations, the constant orientation workspace and the singularity configurations are investigated. The principal contribution of this study is the determination of the workspace based on algebraic geometry (Bohemian domes) and the study of the the singularity configurations. Based on the results, some optimization hints are proposed to refine the kinematic properties.

scholarly journals Kinematic design of a translational parallel mechanism based on sub-kinematic chain determined workspace superposition

2021 ◽  
pp. 095440622110046
Author(s):  
Huiping Shen ◽  
Yinan Zhao ◽  
Guanglei Wu ◽  
Ju Li ◽  
Damien Chablat
Keyword(s):  
Parallel Mechanism ◽  
Kinematic Chain ◽  
Inverse Kinematic ◽  
Parallel Mechanisms ◽  
Kinematic Modeling ◽  
Symbolic Model ◽  
Kinematic Design ◽  
Decoupled Motion ◽  
Topological Characteristics ◽  
Kinematic Solution

This paper presents the kinematic design of a translational parallel mechanism (PM) named Vari-Orthoglide by means of the workspace superposition, according to the sub-kinematic chain (SKC) based PM composition principle. The main topological characteristics of the manipulator with two SKCs under study, such as the position and orientation (POC) characteristics, degree of freedom (DOF) and coupling degree are analyzed, which turns out that the coupling degree equals to 1, implying the partially decoupled motion. With the topological characteristics based kinematic modeling principle, a symbolic model of the kinematics is established to derive its symbolic direct and inverse kinematic solutions. Based upon the direct kinematic solution, the workspaces for the two SKCs can be efficiently found. Moreover, the singularity loci are identified for finding the singularity-free workspace, where a regular workspace is fitted as the task workspace as expected. The presented work shows an approach to design translational parallel mechanisms considering motion decoupling and regular workspace, applicable to other types of parallel mechanisms.

scholarly journals Type Synthesis of 1T2R Parallel Mechanisms Using Structure Coupling-Reducing Method

2019 ◽  
Vol 32 (1) ◽  
Author(s):  
Haitao Liu ◽  
Ke Xu ◽  
Huiping Shen ◽  
Xianlei Shan ◽  
Tingli Yang
Keyword(s):  
Explicit Form ◽  
Parallel Mechanism ◽  
Analytic Solutions ◽  
Forward Kinematics ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Real Time Control ◽  
Time Control ◽  
Topological Characteristics ◽  
Zero Coupling

Abstract Direct kinematics with analytic solutions is critical to the real-time control of parallel mechanisms. Therefore, the type synthesis of a mechanism having explicit form of forward kinematics has become a topic of interest. Based on this purpose, this paper deals with the type synthesis of 1T2R parallel mechanisms by investigating the topological structure coupling-reducing of the 3UPS&UP parallel mechanism. With the aid of the theory of mechanism topology, the analysis of the topological characteristics of the 3UPS&UP parallel mechanism is presented, which shows that there are highly coupled motions and constraints amongst the limbs of the mechanism. Three methods for structure coupling-reducing of the 3UPS&UP parallel mechanism are proposed, resulting in eight new types of 1T2R parallel mechanisms with one or zero coupling degree. One obtained parallel mechanism is taken as an example to demonstrate that a mechanism with zero coupling degree has an explicit form for forward kinematics. The process of type synthesis is in the order of permutation and combination; therefore, there are no omissions. This method is also applicable to other configurations, and novel topological structures having simple forward kinematics can be obtained from an original mechanism via this method.

scholarly journals Design of Self-Reconfigurable Multiarm Robot Mechanism Based on Deployable Kinematic Chains

2020 ◽  
Vol 33 (1) ◽  
Author(s):  
Fu-Qun Zhao ◽  
Sheng Guo ◽  
Hai-Jun Su ◽  
Hai-Bo Qu ◽  
Ya-Qiong Chen
Keyword(s):  
Parallel Mechanism ◽  
Parallel Mechanisms ◽  
Kinematic Chains ◽  
Assembly Method ◽  
Operation Modes ◽  
Object Based ◽  
Switch Operation ◽  
Storage Area ◽  
Mechanism Theory

Abstract As the structures of multiarm robots are serially arranged, the packaging and transportation of these robots are often inconvenient. The ability of these robots to operate objects must also be improved. Addressing this issue, this paper presents a type of multiarm robot that can be adequately folded into a designed area. The robot can achieve different operation modes by combining different arms and objects. First, deployable kinematic chains (DKCs) are designed, which can be folded into a designated area and be used as an arm structure in the multiarm robot mechanism. The strategy of a platform for storing DKCs is proposed. Based on the restrictions in the storage area and the characteristics of parallel mechanisms, a class of DKCs, called base assembly library, is obtained. Subsequently, an assembly method for the synthesis of the multiarm robot mechanism is proposed, which can be formed by the connection of a multiarm robot mechanism with an operation object based on a parallel mechanism structure. The formed parallel mechanism can achieve a reconfigurable characteristic when different DKCs connect to the operation object. Using this method, two types of multiarm robot mechanisms with four DKCs that can switch operation modes to perform different tasks through autonomous combination and release operation is proposed. The obtained mechanisms have observable advantages when compared with the traditional mechanisms, including optimizing the occupied volume during transportation and using parallel mechanism theory to analyze the switching of operation modes.

scholarly journals Constraint and Mobility Change Analysis of Rubik’s Cube-inspired Reconfigurable Joints and Corresponding Parallel Mechanisms

2020 ◽  
Vol 33 (1) ◽  
Author(s):  
Duanling Li ◽  
Pu Jia ◽  
Jiazhou Li ◽  
Dan Zhang ◽  
Xianwen Kong
Keyword(s):  
Parallel Mechanism ◽  
Unique Feature ◽  
Theoretical Method ◽  
Geometric Constraint ◽  
Parallel Mechanisms ◽  
Change Analysis ◽  
Application Range ◽  
And Topology ◽  
Physical Experiments ◽  
Underlying Principle

Abstract The current research of reconfigurable parallel mechanism mainly focuses on the construction of reconfigurable joints. Compared with the method of changing the mobility by physical locking joints, the geometric constraint has good controllability, and the constructed parallel mechanism has more configurations and wider application range. This paper presents a reconfigurable axis (rA) joint inspired and evolved from Rubik's Cubes, which have a unique feature of geometric and physical constraint of axes of joint. The effectiveness of the rA joint in the construction of the limb is analyzed, resulting in a change in mobility and topology of the parallel mechanism. The rA joint makes the angle among the three axes inside the groove changed arbitrarily. This change in mobility is completed by the case illustrated by a 3(rA)P(rA) reconfigurable parallel mechanism having variable mobility from 1 to 6 and having various special configurations including pure translations, pure rotations. The underlying principle of the metamorphosis of this rA joint is shown by investigating the dependence of the corresponding screw system comprising of line vectors, leading to evolution of the rA joint from two types of spherical joints to three types of variable Hooke joints and one revolute joint. The reconfigurable parallel mechanism alters its topology by rotating or locking the axis of rA joint to turn all limbs into different phases. The prototype of reconfigurable parallel mechanism is manufactured and all configurations are enumerated to verify the validity of the theoretical method by physical experiments.

Analytic Determination of Wrench Closure Workspace of Spatial Cable Driven Parallel Mechanisms

2015 ◽  
Author(s):  
Zhiyu Sheng ◽  
Joon-Hyuk Park ◽  
Paul Stegall ◽  
Sunil K. Agrawal
Keyword(s):  
Simulation Study ◽  
Null Space ◽  
Boundary Surface ◽  
Parallel Mechanisms ◽  
Analytic Determination ◽  
Structure Matrix ◽  
Feasible Solutions

This paper proposes an efficient way of determining analytically the Wrench Closure Workspace (WCW) of spatial redundant cable-driven parallel mechanisms (CDPM). The method builds upon the boundary surface equations obtained from the null space of the structure matrix of CDPM. The set of feasible solutions is obtained that satisfies positive tension in the cables. This method was applied to characterize the WCW of spatial CDPM which has redundancy of 1 or 2. A simulation study was carried out to validate the accuracy and efficiency of the method. Several advantages over conventional approaches for determining the WCW were identified through simulation.

Evaluation and Representation of the Theoretical Orientation Workspace of the Gough–Stewart Platform

2009 ◽  
Vol 1 (2) ◽  
Author(s):  
Qimi Jiang ◽  
Clément M. Gosselin
Keyword(s):  
Theoretical Orientation ◽  
Robotic Manipulators ◽  
Stewart Platform ◽  
Closed Region ◽  
Leg Length ◽  
Fixed Frame ◽  
Cartesian Space ◽  
Orientation Workspace

The evaluation and representation of the orientation workspace of robotic manipulators is a challenging task. This work focuses on the determination of the theoretical orientation workspace of the Gough–Stewart platform with given leg length ranges [ρimin,ρimax]. By use of the roll-pitch-yaw angles (ϕ,θ,ψ), the theoretical orientation workspace at a prescribed position P0 can be defined by up to 12 workspace surfaces. The defined orientation workspace is a closed region in the 3D orientation Cartesian space Oϕθψ. As all rotations R(x,ϕ), R(y,θ), and R(z,ψ) take place with respect to the fixed frame, any point of the defined orientation workspace provides a clear measure for the platform to, respectively, rotate in order around the (x,y,z) axes of the fixed frame. An algorithm is presented to compute the size (volume) of the theoretical orientation workspace and intersectional curves of the workspace surfaces. The defined theoretical orientation workspace can be applied to determine a singularity-free orientation workspace.

scholarly journals Dynamic response analysis for multi-degrees-of-freedom parallel mechanisms with various types of three-dimensional clearance joints

2021 ◽  
Vol 18 (3) ◽  
pp. 172988142110177
Author(s):  
Jia Yonghao ◽  
Chen Xiulong
Keyword(s):  
Dynamic Response ◽  
Multibody Systems ◽  
Parallel Mechanism ◽  
Three Dimensional ◽  
Response Analysis ◽  
Parallel Mechanisms ◽  
Dynamics Model ◽  
Clearance Joints ◽  
Clearance Joint ◽  
Spatial Parallel Mechanism

For spatial multibody systems, the dynamic equations of multibody systems with compound clearance joints have a high level of nonlinearity. The coupling between different types of clearance joints may lead to abundant dynamic behavior. At present, the dynamic response analysis of the spatial parallel mechanism considering the three-dimensional (3D) compound clearance joint has not been reported. This work proposes a modeling method to investigate the influence of the 3D compound clearance joint on the dynamics characteristics of the spatial parallel mechanism. For this purpose, 3D kinematic models of spherical clearance joint and revolute joint with radial and axial clearances are derived. Contact force is described as normal contact and tangential friction and later introduced into the nonlinear dynamics model, which is established by the Lagrange multiplier technique and Jacobian of constraint matrix. The influences of compound clearance joint and initial misalignment of bearing axes on the system are analyzed. Furthermore, validation of dynamics model is evaluated by ADAMS and Newton–Euler method. This work provides an essential theoretical basis for studying the influences of 3D clearance joints on dynamic responses and nonlinear behavior of parallel mechanisms.

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