scholarly journals STRUCTURAL SYNTHESIS OF PARALLEL MECHANISMS THAT PROVIDE PLANE-PARALLEL MOTION OF THE OUTPUT LINK BASED ON THE THEORY OF SCREWS AND VIRTUAL KINEMATIC CHAINS

2016 ◽  
Vol 2 (1) ◽  
pp. 185-194
Author(s):  
Гапоненко ◽  
Elena Gaponenko ◽  
Рыбак ◽  
Larisa Rybak ◽  
Малышев ◽  
...  
Keyword(s):  
Kinematic Chain ◽  
Parallel Mechanisms ◽  
Structural Synthesis ◽  
Output Link ◽  
Kinematic Chains ◽  
Plane Parallel ◽  
Parallel Movement ◽  
Parallel Motion ◽  
Movable Platform ◽  
Virtual Circuits

This article describes the method of structural synthesis of a class of parallel mechanisms that provide plane-parallel movement of the movable platform. The considered method is based on the theory of screws and the concept of virtual circuits. We obtain the structure of parallel mechanisms, containing three connecting kinematic chain.

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.

Designing Statically Determinable Mechanisms of Technological Mechatronic Machines with Parallel Kinematics

2019 ◽  
Vol 20 (7) ◽  
pp. 428-436
Author(s):  
A. K. Tolstosheev ◽  
V. A. Tatarintsev
Keyword(s):  
Structural Analysis ◽  
Hierarchical Structure ◽  
Degrees Of Freedom ◽  
Kinematic Chain ◽  
Parallel Structure ◽  
Parallel Kinematics ◽  
Output Link ◽  
Parallel Connection ◽  
Kinematic Chains ◽  
Chain Increase

The work is devoted to improving the reliability and manufacturability of mechatronic machine designs with parallel kinematics by replacing statically indeterminable manipulators with statically determinable mechanisms. A technique is proposed in which the design of statically determinable manipulators of technological mechatronic machines with parallel kinematics is performed by modifying the structure of prototypes and includes three steps: identifying and analyzing redundant links, eliminating redundant links, checking the correctness of eliminating redundant links. To determine the number of degrees of freedom of the mechanism, identify redundant links, and verify the solution, the authors use the proposed methodology for structural analysis of parallel structure mechanisms. In structural analysis, a manipulator is represented by a hierarchical structure and is considered as a parallel connection of elementary mechanisms with an open kinematic chain; as a kinematic chain consisting of leading and driven parts; as a set of links and kinematic pairs; as a kinematic connection of the output link and the rack. The article implements the following techniques for eliminating redundant links: mobility increase in kinematic pairs; introduction of unloading links and passive kinematic pairs to the kinematic chain; exclusion of extra links and pairs from the kinematic chain; increase in mobility in some kinematic pairs simultaneously with the exclusion of other kinematic pairs that have become superfluous. The authors developed several variants of structural schemes of self-aligning manipulators based on the Orthoglide mechanism, which retain the basic functional proper ties of the prototype. To increase the number of self-aligning mechanism diagrams, the redistribution of mobilities and links within the connecting kinematic chain and between connecting kinematic chains is used. The proposed methodics allow to determine the number of degrees of freedom of the mechanism, the number and type of redundant links, eliminate redundant links and, on an alternative basis, build structural diagrams of statically determinable mechanisms of technological mechatronic machines with parallel kinematics.

Critical Review of Existing Degeneracy Testing and Mobility Type Identification Algorithms for Kinematic Chains

2005 ◽  
Author(s):  
Rajesh Pavan Sunkari ◽  
Linda C. Schmidt
Keyword(s):  
Critical Review ◽  
Kinematic Chain ◽  
Structural Studies ◽  
Mobility Analysis ◽  
Structural Synthesis ◽  
Common Error ◽  
Kinematic Chains ◽  
The Individual ◽  
Almost All ◽  
Mathematical Justification

Mobility analysis is one of the fundamental problems of structural studies of kinematic chains. Degeneracy testing, an important step in structural synthesis, can be considered as a part of the mobility analysis due to the similarity of the two problems. One common error in the algorithms for these two problems is the assumption that the graph of a planar kinematic chain is a planar graph. This work shows that almost all the mobility analysis algorithms, except that of Lee and Yoon, have this error. This work also critically reviews the two most efficient algorithms on degeneracy testing, those by Hwang and Hwang, and Lee and Yoon. It is shown that due to the errors in the Hwang and Hwang’s algorithm, it failed to identify some of the degenerate chains. Furthermore, the accuracy of the Lee and Yoon’s algorithms for mobility analysis and degeneracy testing is proved by providing the mathematical justification of the individual steps of the algorithms.

scholarly journals OPTIONS FOR PLANE-PARALLEL MOVEMENT OF GRAINS IN A SCRAPER CONVEYOR

2020 ◽  
Vol 14 (4) ◽  
pp. 96-99
Author(s):  
Sergey Yakhin ◽  
Il'gam Masalimov ◽  
Marat Nafikov ◽  
Ramis Mardanov
Keyword(s):  
Complex Motion ◽  
Sliding Speed ◽  
Friction Forces ◽  
Plane Parallel ◽  
Parallel Movement ◽  
Parallel Motion ◽  
Touch Point ◽  
Scraper Conveyor ◽  
Instantaneous Center ◽  
Kinematic Diagram

The kinematics of plane-parallel motion of a wheat or rye grain when moving in an inclined position in a scraper conveyor is considered. A kinematic diagram of the plane-parallel motion of the grain in the scraper conveyor was compiled, the position of the instantaneous center of the flat figure was determined, and options for the movement of grain in an inclined position at various possible positions of instantaneous center were considered. The profile of the grains is outlined by an elliptical curve. The point of contact of the elliptical profile of the caryopsis with the scraper makes a complex motion, while the horizontal speed of the scraper is portable for it, the sliding speed on the surface of the scraper is relative. The speed of the touch point of the grain with the pan is horizontal. For six possible positions of the instantaneous center, the directions of the velocities of the points of contact of the grains and the friction forces acting in them are determined. Grains of wheat or rye, moved in a scraper conveyor, in some cases can make plane-parallel movement. The point of contact of the elliptical profile of the caryopsis with the scraper makes a complex motion, while the horizontal speed of the scraper is portable for it, the sliding speed on the surface of the scraper is relative. The speed of the touch point 2 of the grain with the pan is horizontal.

Topological Characteristics and Automatic Generation of Structural Synthesis of Spatial Mechanisms: Part II — Automatic Generation of Structural Types of Kinematic Chains

1992 ◽  
Author(s):  
Ting-Li Yang ◽  
Fang-Hua Yao
Keyword(s):  
Kinematic Chain ◽  
Automatic Generation ◽  
Structural Synthesis ◽  
Kinematic Chains ◽  
Automatic Program ◽  
Spatial Mechanisms ◽  
Structural Types ◽  
Topological Characteristics ◽  
Linear Graphs ◽  
Independent Loops

Abstract Based on the single-opened chain constraints and the network topological characteristics of mechanisms, a powerful new method for structural synthesis of spatial kinematic chain with plane and nonplane linear graphs has been developed. This permits the development of a highly efficient and completely automatic program for the computer-generated enumeration of structural types of mechanisms. The method is illustrated by applying to the case of kinematic chains with up to six independent loops on a personal computer.

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.

THE PROPERTIES OF THE MECHANISMS WITH SIX DEGREES OF FREEDOM

2021 ◽  
pp. 28-33
Author(s):  
S. V. Kheylo ◽  
O. A. Garin ◽  
S. V. Palochkin ◽  
S. D. Dorofeev
Keyword(s):  
Degrees Of Freedom ◽  
The Novel ◽  
Parallel Mechanisms ◽  
Kinematic Scheme ◽  
Output Link ◽  
Kinematic Chains ◽  
Analysis And Design ◽  
Six Degrees Of Freedom ◽  
Robotic Assisted Surgery ◽  
Coupling Equations

Parallel mechanisms analysis and design are the main trends of advance robotic engineering. This article is devoted to the novel parallel mechanisms with six degrees of freedom. The presented mechanisms can be applied in additive technologies, robotic–assisted surgery. The proposed mechanisms contain six drives and six kinematic chains. They have the properties of a partial kinematic decoupling, which allows realized separately translational and rotational movements. The presented mechanisms is a simple kinematic scheme. The drives can provide a ratio 1:1 of with the movement of the output link. The paper considers the solution of kinematics problems, velocity analysis, singularities. The velocity problem is solved by differentiating the coupling equations. Singularities were detected by studying the properties of Jacobi matrices. The singularities depend only on the orientation of the output link. These mechanisms have a large working area free of singularities. The working area is determined by solving the coupling equations. The solved problems allow to solve the control such mechanisms in the future.

A More Direct Method for Structural Synthesis of Simple-Jointed Planar Kinematic Chains

1994 ◽  
Author(s):  
Varada Raju Dharanipragada ◽  
Nagaraja Kumar Yenugadhati ◽  
A. C. Rao
Keyword(s):  
Graph Theory ◽  
Computer Program ◽  
Reliable Method ◽  
Direct Method ◽  
Kinematic Chain ◽  
Degree Of Freedom ◽  
Structural Synthesis ◽  
Indirect Methods ◽  
Kinematic Chains ◽  
A Chain

Abstract Structural synthesis of kinematic chains leans heavily on indirect methods, most of them based on Graph Theory, mainly because reliable isomorphism tests are not available. Recently however, the first and third authors have established the Secondary Hamming String of a kinematic chain as an excellent indicator of its isomorphism. In the present paper this Hamming String method was applied with slight modifications for synthesizing on a PC-386, distinct kinematic chains with given number of links and family description. The computer program, written in Pascal, generated both the six-bar and all 16 eight-bar chains as well as one sample family (2008) of ten-bar chains, verifying previously established results. Hence this paper presents a direct, quick and reliable method to synthesize planar simple-jointed chains, open or closed, with single- or multi-degree of freedom, containing any number of links. A spin-off of this paper is a simple, concise and unambiguous notation for representing a chain.

scholarly journals Mathematical Model of the Plane-Parallel Movement of the Self-Propelled Root-Harvesting Machine

2018 ◽  
Vol 10 (10) ◽  
pp. 3614 ◽  
Author(s):  
Volodymyr Bulgakov ◽  
Simone Pascuzzi ◽  
Francesco Santoro ◽  
Alexandros Anifantis
Keyword(s):  
Mathematical Model ◽  
Experimental Tests ◽  
Quality Parameters ◽  
The Self ◽  
Crop Damage ◽  
Root Crop ◽  
Plane Parallel ◽  
Parallel Movement ◽  
Parallel Motion ◽  
Harvest Techniques

The harvest techniques and the employed machines are important factors in reducing soil loss due to root crop harvesting. Furthermore, the deviation of the working organs of the self-propelled sugar root harvesting machines from the axis of the row also leads to significant losses and damage to sugar beetroots. Therefore, the self-propelled machine units must move in a horizontal plane with a high degree of accuracy. The purpose of this study is to increase the efficiency of the self-propelled harvester by analyzing its plane-parallel motion and evaluating its constructive and kinematic parameters. In order to determine the influence of these parameters on the plane-parallel motion of the self-propelled root harvesting machine, its mathematical model has been calculated. Furthermore, experimental tests were executed in order to evaluate the degree of damage to sugar beetroot crops during their digging, depending on the magnitude of the deviations of the center of the digging tool. The results of this trials highlighted that if the crop row deviates from the conventional axis line by 10 mm, the root crop damage exceeds is 21.7% and at deviations by 70 mm, the damage exceeds 67%. The theoretical study of the trajectory of the center of the outside digging tool and the experimental evaluation of its work (in terms of the quality of harvesting with deviations in its trajectory of motion) formally confirm the coincidence of all the studies—both theoretical and experimental. The use of the model of the plane-parallel movement of the self-propelled root harvesting machine then improves the quality parameters of the technological process.

Position and Orientation Characteristic Equation for Topological Design of Robot Mechanisms

2008 ◽  
Vol 131 (2) ◽  
Author(s):  
Ting-Li Yang ◽  
An-Xin Liu ◽  
Qiong Jin ◽  
Yu-Feng Luo ◽  
Hui-Ping Shen ◽  
...  
Keyword(s):  
Topological Structure ◽  
Kinematic Chain ◽  
Parallel Mechanisms ◽  
Structural Synthesis ◽  
Geometrical Meaning ◽  
Single Loop ◽  
Operation Rules ◽  
The Matrix ◽  
Position And Orientation ◽  
Symbolic Operation

This paper presents the explicit mapping relations between topological structure and position and orientation characteristic (POC) of mechanism motion output. It deals with (1) the symbolic representation and the invariant property of the topological structure of the mechanism, (2) the matrix representation of POC of mechanism motion output, and (3) the POC equations of serial and parallel mechanisms and the corresponding symbolic operation rules. The symbolic operation involves simple mathematic tools and fewer operation rules and has clear geometrical meaning, so it is easy to use. The POC equations cannot only be used for structural analysis of the mechanism (such as determining POC of the relative motion between any two links of a mechanism and the rank of single-loop kinematic chain and calculating the full-cycle DOF of a mechanism, etc.) but can be used for structural synthesis of the mechanism as well (e.g., structural synthesis of the rank-degenerated serial mechanism, the over constrained single-loop mechanism, and the rank-degenerated parallel mechanism, etc.).

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