Product Submanifold Based Analysis of Kinematic Chains and a 3-PUP Parallel Mechanism

2016 ◽  
Author(s):  
Xinsheng Zhang ◽  
Jian S. Dai
Keyword(s):  
Lie Group ◽  
Parallel Mechanism ◽  
Kinematic Chain ◽  
Planar Motion ◽  
Motion Group ◽  
Kinematic Chains ◽  
Prismatic Joint ◽  
Screw Motion ◽  
Joint Axis ◽  
Joint Direction

The five types of kinematic chains that generate the planar motion group SE(2) of dimension three, with the prismatic-joint direction always perpendicular with the revolute-joint axis in each chain, have shown their effectiveness and manifested the charm in type synthesis and mechanism analysis in parallel mechanisms. This paper extends the traditional PRP kinematic chain generating the planar motion group SE(2) to a relatively general case, in which one of the prismatic joint-direction is not necessarily perpendicular with the revolute-joint axis, leading to the discovery of a screw motion with a variable pitch in this kinematic chain. Following the extraction of a screw motion from this particular PRP kinematic chain, this paper presents the bifurcated motion in a 3-PUP parallel mechanism by changing the active geometrical constraint in its configuration space, with a Lie group approach and interpretation. The constraint-singularity configuration sets for bifurcation of the 3-PUP parallel mechanism. The paper hence provides a Lie group representation and geometry interpretation for the kinematic equivalence of serial chains and the bifurcated motion of a parallel mechanism.

Compositional Submanifolds of Prismatic–Universal–Prismatic and Skewed Prismatic–Revolute– Prismatic Kinematic Chains and Their Derived Parallel Mechanisms

2018 ◽  
Vol 10 (3) ◽  
Author(s):  
Xinsheng Zhang ◽  
Pablo López-Custodio ◽  
Jian S. Dai
Keyword(s):  
Parallel Mechanism ◽  
Kinematic Chain ◽  
Planar Motion ◽  
Helical Motion ◽  
Parallel Mechanisms ◽  
Motion Group ◽  
Revolute Joint ◽  
Kinematic Chains ◽  
Prismatic Joint ◽  
Joint Axis

The kinematic chains that generate the planar motion group in which the prismatic-joint direction is always perpendicular to the revolute-joint axis have shown their effectiveness in type synthesis and mechanism analysis in parallel mechanisms. This paper extends the standard prismatic–revolute–prismatic (PRP) kinematic chain generating the planar motion group to a relatively generic case, in which one of the prismatic joint-directions is not necessarily perpendicular to the revolute-joint axis, leading to the discovery of a pseudo-helical motion with a variable pitch in a kinematic chain. The displacement of such a PRP chain generates a submanifold of the Schoenflies motion subgroup. This paper investigates for the first time this type of motion that is the variable-pitched pseudo-planar motion described by the above submanifold. Following the extraction of a helical motion from this skewed PRP kinematic chain, this paper investigates the bifurcated motion in a 3-prismatic–universal–prismatic (PUP) parallel mechanism by changing the active geometrical constraint in its configuration space. The method used in this contribution simplifies the analysis of such a parallel mechanism without resorting to an in-depth geometrical analysis and screw theory. Further, a parallel platform which can generate this skewed PRP type of motion is presented. An experimental test setup is based on a three-dimensional (3D) printed prototype of the 3-PUP parallel mechanism to detect the variable-pitched translation of the helical motion.

Dexterous Workspace of n-PRRR Planar Parallel Manipulators

2012 ◽  
Vol 4 (3) ◽  
Author(s):  
André Gallant ◽  
Roger Boudreau ◽  
Marise Gallant
Keyword(s):  
Kinematic Chain ◽  
Parallel Manipulators ◽  
Divergence Theorem ◽  
End Effector ◽  
Kinematic Chains ◽  
Prismatic Joint ◽  
Planar Surfaces ◽  
Revolute Joints ◽  
Gauss Divergence Theorem ◽  
Planar Parallel Manipulators

In this work, a method is presented to geometrically determine the dexterous workspace boundary of kinematically redundant n-PRRR (n-PRRR indicates that the manipulator consists of n serial kinematic chains that connect the base to the end-effector. Each chain is composed of two actuated (therefore underlined) joints and two passive revolute joints. P indicates a prismatic joint while R indicates a revolute joint.) planar parallel manipulators. The dexterous workspace of each nonredundant RRR kinematic chain is first determined using a four-bar mechanism analogy. The effect of the prismatic actuator is then considered to yield the workspace of each PRRR kinematic chain. The intersection of the dexterous workspaces of all the kinematic chains is then obtained to determine the dexterous workspace of the planar n-PRRR manipulator. The Gauss divergence theorem applied to planar surfaces is implemented to compute the total dexterous workspace area. Finally, two examples are shown to demonstrate applications of the method.

A geometrical formulation for the workspace of parallel manipulators

Robotica ◽  
2021 ◽  
pp. 1-11
Author(s):  
Matteo Russo ◽  
Marco Ceccarelli
Keyword(s):  
Parallel Mechanism ◽  
Parallel Manipulator ◽  
Kinematic Chain ◽  
Parallel Manipulators ◽  
Analytical Models ◽  
Kinematic Chains ◽  
Motion Constraints ◽  
Geometrical Formulation ◽  
Geometric Formulation ◽  
Algebraic Formulation

Abstract In study this paper, a geometric formulation is proposed to describe the workspace of parallel manipulators by using a recursive approach as an extension of volume generation for solids of revolution. In this approach, the workspace volume and boundary for each limb of the parallel manipulator is obtained with an algebraic formulation derived from the kinematic chain of the limb and the motion constraints on its joints. Then, the overall workspace of the mechanism can be determined as the intersection of the limb workspaces. The workspace of different kinematic chains is discussed and classified according to its external shape. An algebraic formulation for the inclusion of obstacles in the computation is also proposed. Both analytical models and numerical simulations are reported with their advantages and limitations. An example on a 3-SPR parallel mechanism illustrates the feasibility of the formulation and its efficiency.

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.

Structure Based Grading of Kinematic Chains

2014 ◽  
Vol 575 ◽  
pp. 501-506 ◽  
Author(s):  
Shubhashis Sanyal ◽  
G.S. Bedi
Keyword(s):  
Structural Properties ◽  
Structural Property ◽  
Kinematic Chain ◽  
Degree Of Freedom ◽  
Kinematic Chains ◽  
Structural Differences ◽  
The Individual ◽  
Independent Loops

Kinematic chains differ due to the structural differences between them. The location of links, joints and loops differ in each kinematic chain to make it unique. Two similar kinematic chains will produce similar motion properties and hence are avoided. The performance of these kinematic chains also depends on the individual topology, i.e. the placement of its entities. In the present work an attempt has been made to compare a family of kinematic chains based on its structural properties. The method is based on identifying the chains structural property by using its JOINT LOOP connectivity table. Nomenclature J - Number of joints, F - Degree of freedom of the chain, N - Number of links, L - Number of basic loops (independent loops plus one peripheral loop).

scholarly journals Topological Design of an Asymmetric 3-Translational Parallel Mechanism With Zero Coupling Degree and Motion Decoupling

2018 ◽  
Author(s):  
Huiping Shen ◽  
Chengqi Wu ◽  
Damien Chablat ◽  
Guanglei Wu ◽  
Ting-li Yang
Keyword(s):  
Parallel Mechanism ◽  
Design Theory ◽  
Analytical Formula ◽  
Inverse Kinematic ◽  
Topology Design ◽  
Kinematic Chains ◽  
Topological Design ◽  
Decoupled Motion ◽  
Topological Characteristics ◽  
Zero Coupling

In this paper a new asymmetric 3-translational (3T) parallel manipulator, i.e., RPa(3R) 2R+RPa, with zero coupling degree and decoupled motion is firstly proposed according to topology design theory of parallel mechanism (PM) based on position and orientation characteristics (POC) equations. The main topological characteristics such as POC, degree of freedom and coupling degree are calculated. Then, the analytical formula for the direct and inverse kinematic are directly derived since coupling degree of the PM is zero. The study of singular configurations is simple because of the independence of the kinematic chains.

Combined Graph Layout Algorithms for Automated Sketching of Kinematic Chains

2012 ◽  
Author(s):  
Martín A. Pucheta ◽  
Nicolás E. Ulrich ◽  
Alberto Cardona
Keyword(s):  
Computational Cost ◽  
Kinematic Chain ◽  
Initial Position ◽  
Graph Representation ◽  
Combinatorial Algorithms ◽  
Graph Layout ◽  
Kinematic Chains ◽  
Aesthetic Characteristics ◽  
Edge Crossings ◽  
Independent Loops

The graph layout problem arises frequently in the conceptual stage of mechanism design, specially in the enumeration process where a large number of topological solutions must be analyzed. Two main objectives of graph layout are the avoidance or minimization of edge crossings and the aesthetics. Edge crossings cannot be always avoided by force-directed algorithms since they reach a minimum of the energy in dependence with the initial position of the vertices, often randomly generated. Combinatorial algorithms based on the properties of the graph representation of the kinematic chain can be used to find an adequate initial position of the vertices with minimal edge crossings. To select an initial layout, the minimal independent loops of the graph can be drawn as circles followed by arcs, in all forms. The computational cost of this algorithm grows as factorial with the number of independent loops. This paper presents a combination of two algorithms: a combinatorial algorithm followed by a force-directed algorithm based on spring repulsion and electrical attraction, including a new concept of vertex-to-edge repulsion to improve aesthetics and minimize crossings. Atlases of graphs of complex kinematic chains are used to validate the results. The layouts obtained have good quality in terms of minimization of edge crossings and maximization of aesthetic characteristics.

A Novel Method for Constructing Multi-Mode Deployable Polyhedron Mechanisms Using Symmetric Spatial RRR Compositional Units

2018 ◽  
Author(s):  
Jieyu Wang ◽  
Xianwen Kong
Keyword(s):  
Kinematic Chain ◽  
Degree Of Freedom ◽  
Single Loop ◽  
Kinematic Chains ◽  
The Third ◽  
Motion Modes ◽  
3D Printed ◽  
Novel Method ◽  
Multi Mode ◽  
Motion Mode

A novel construction method is proposed to construct multimode deployable polyhedron mechanisms (DPMs) using symmetric spatial RRR compositional units, a serial kinematic chain in which the axes of the first and the third revolute (R) joints are perpendicular to the axis of the second R joint. Single-loop deployable linkages are first constructed using RRR units and are further assembled into polyhedron mechanisms by connecting single-loop kinematic chains using RRR units. The proposed mechanisms are over-constrained and can be deployed through two approaches. The prism mechanism constructed using two Bricard linkages and six RRR limbs has one degree-of-freedom (DOF). When removing three of the RRR limbs, the mechanism obtains one additional 1-DOF motion mode. The DPMs based on 8R and 10R linkages also have multiple modes, and several mechanisms are variable-DOF mechanisms. The DPMs can switch among different motion modes through transition positions. Prototypes are 3D-printed to verify the feasibility of the mechanisms.

scholarly journals A Recursive Algorithm for the Forward Kinematic Analysis of Robotic Systems Using Euler Angles

Robotics ◽  
2022 ◽  
Vol 11 (1) ◽  
pp. 15
Author(s):  
Fernando Gonçalves ◽  
Tiago Ribeiro ◽  
António Fernando Ribeiro ◽  
Gil Lopes ◽  
Paulo Flores
Keyword(s):  
Recursive Algorithm ◽  
Kinematic Chain ◽  
Robotic Systems ◽  
Mobile Manipulator ◽  
Euler Angles ◽  
Joint Angles ◽  
Main Research ◽  
Kinematic Chains ◽  
Research Fields ◽  
Forward Kinematic

Forward kinematics is one of the main research fields in robotics, where the goal is to obtain the position of a robot’s end-effector from its joint parameters. This work presents a method for achieving this using a recursive algorithm that builds a 3D computational model from the configuration of a robotic system. The orientation of the robot’s links is determined from the joint angles using Euler Angles and rotation matrices. Kinematic links are modeled sequentially, the properties of each link are defined by its geometry, the geometry of its predecessor in the kinematic chain, and the configuration of the joint between them. This makes this method ideal for tackling serial kinematic chains. The proposed method is advantageous due to its theoretical increase in computational efficiency, ease of implementation, and simple interpretation of the geometric operations. This method is tested and validated by modeling a human-inspired robotic mobile manipulator (CHARMIE) in Python.

scholarly journals Structural synthesis of plane kinematic chain inversions without detecting isomorphism

2021 ◽  
Vol 12 (2) ◽  
pp. 1061-1071
Author(s):  
Jinxi Chen ◽  
Jiejin Ding ◽  
Weiwei Hong ◽  
Rongjiang Cui
Keyword(s):  
Mechanism Design ◽  
Adjacency Matrix ◽  
Synthesis Method ◽  
Kinematic Chain ◽  
Degree Of Freedom ◽  
Synthesis Methods ◽  
Creative Design ◽  
Structural Synthesis ◽  
Kinematic Chains

Abstract. A plane kinematic chain inversion refers to a plane kinematic chain with one link fixed (assigned as the ground link). In the creative design of mechanisms, it is important to select proper ground links. The structural synthesis of plane kinematic chain inversions is helpful for improving the efficiency of mechanism design. However, the existing structural synthesis methods involve isomorphism detection, which is cumbersome. This paper proposes a simple and efficient structural synthesis method for plane kinematic chain inversions without detecting isomorphism. The fifth power of the adjacency matrix is applied to recognize similar vertices, and non-isomorphic kinematic chain inversions are directly derived according to non-similar vertices. This method is used to automatically synthesize 6-link 1-degree-of-freedom (DOF), 8-link 1-DOF, 8-link 3-DOF, 9-link 2-DOF, 9-link 4-DOF, 10-link 1-DOF, 10-link 3-DOF and 10-link 5-DOF plane kinematic chain inversions. All the synthesis results are consistent with those reported in literature. Our method is also suitable for other kinds of kinematic chains.

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