Linear Delta Robot Research Articles

Extended CODAS method for MAGDM with $ 2 $-tuple linguistic $ T $-spherical fuzzy sets

<abstract><p>In the literature, extensions of common fuzzy sets have been proposed one after another. The recent addition is spherical fuzzy sets theory, which is based on three independent membership parameters established on a unit sphere with a restriction linked to their squared summation. This article uses the new extension that presents bigger domains for each parameter for production design. A systematic approach for determining customer demands or requirements, Quality Function Deployment (QFD) converts them into the final production to fulfill these demands in a decision-making environment. In order to prevent information loss during the decision-making process, it offers a useful technique to describe the linguistic analysis in terms of 2-tuples. This research introduces a novel decision-making method utilizing the 2-tuple linguistic $ T $-spherical fuzzy numbers (2TL$ T $-SFNs) in order to select the best alternative to manufacturing a linear delta robot. Taking into account the interaction between the attributes, we develop the 2TL$ T $-SF Hamacher (2TL$ T $-SFH) operators by using innovative operational rules. These operators include the 2TL$ T $-SFH weighted average (2TL$ T $-SFHWA) operator, 2TL$ T $-SFH ordered weighted average (2TL$ T $-SFHOWA) operator, 2TL$ T $-SFH hybrid average (2TL$ T $-SFHHA) operator, 2TL$ T $-SFH weighted geometric (2TL$ T $-SFHWG) operator, 2TL$ T $-SFH ordered weighted geometric (2TL$ T $-SFHOWG) operator, and 2TL$ T $-SFH hybrid geometric (2TL$ T $-SFHHG) operator. In addition, we discuss the properties of 2TL$ T $-SFH operators such as idempotency, boundedness, and monotonicity. We develop a novel approach according to the CODAS (Combinative Distance-based Assessment) model in order to deal with the problems of the 2TL$ T $-SF multi-attribute group decision-making (MAGDM) environment. Finally, to validate the feasibility of the given strategy, we employ a quantitative example to select the best alternative to manufacture a linear delta robot. The suggested information-based decision-making methodology which is more extensively adaptable than existing techniques prevents the risk of data loss and makes rational decisions.</p></abstract>

Linear Delta Robot Controlled with PLC Based On Image Processing

Delta Robot is taking an important place in industry 4.0. Its ability to work fast and with precision is the reason why this robot now is used worldwide in the industrial field. Delta robots are mostly used for packaging, 3D printing, pick and place, etc. This robot can be controlled using programmable logic controller (PLC) devices. In recent years, image processing methods have been widely used in many robot applications. In this study, it is aimed to ensure that the robot successfully moves to the determined points by using image processing methods. Images for this study were obtained by attaching a camera to the robot system. In this study, the aim is to set the robot to move based on the visual data that is taken by the camera. The coordinates of each object are defined after several steps in image processing. To be able to move the robot to the desired coordinates, inverse and forward kinematic analysis is proposed. The obtained values are transferred to PLC using OPC. The necessary coding in TIA Portal is done to control the motor drivers so that the three stepper motors can ensure the delta robot moves to the desired coordinate position.

Design and implementation of a 3D photocopier with photogrammetric method using linear delta robot

در مقاله‌ی حاضر به طراحی و ساخت دستگاه فتوکپی سه‌بعدی پرداخته شده است. این دستگاه دارای دو واحد اصلی می باشد که عبارتند از: واحد اسکنر سه‌بعدی و واحد چاپگر سه‌بعدی. امروزه نیاز به استفاده از اسکنرهای سه‌بعدی در کاربردهای مختلف نظیر کنترل کیفیت، مهندسی معکوس و طراحی و تولید به کمک کامپیوتر در حال گسترش است. این دستگاه قادر خواهد بود اسکن سه‌بعدی بگیرد و پس از پردازش تصویر اسکن‌شده، یک مدل سه‌بعدی جهت چاپ به واحد چاپگر سه‌بعدی ارسال کند و یک مدل کپی از آن قطعه بسازد. از مزایای برجسته‌ی این طرح استفاده از آن در مهندسی معکوس می‌باشد که می‌تواند یک مدل کپی با تناسب دلخواه از یک قطعه را بدون نیاز به فرایند اندازه‌گیری جهت تعیین ابعاد و به‌دنبال آن فرایند طراحی که بعضاً در بسیاری از موارد به‌دلیل پیچیدگی‌های ظاهری قطعه‌، کاری طولانی، سخت و زمان بر است، در کمترین زمان بسازد. این امکان فراهم شده که بعد از گرفتن اسکن از قطعه در صورت نیاز به ترمیم یا تغییر، اصلاح صورت گیرد و بعد به واحد چاپگر سه‌بعدی ارسال شود. اسکن قطعه از روش فوتوگرامتری بهره گرفته است. چاپگرهای سه‌بعدی با مکانیزم‌‌ها و فناوری‌های مختلف کار می‌کنند. مکانیزم حرکتی چاپگر با الهام از مکانیزم ربات دلتا و فناوری چاپ اکسترود (ذوب) مواد اولیه انتخاب شده است. به بیان قواعد و اصول طراحی و ساخت یک چاپگر سه‌بعدی پرداخته می‌شود و بیان می‌شود که چگونه رعایت این اصول و قواعد در افزایش دقت و کیفیت قطعات تولیدی تاثیر‌گذار خواهند ‌بود.

General Procedure for Servo-Axis Design in Multi-Degree-of-Freedom Machinery Subject to Mixed Loads

The motion performances of multi-axis machinery are strongly related to the proper design of the servo axes driving the actuated joints, which must fulfil motion requests in terms of speed and torque for the motion design task. Multi-degree-of-freedom machinery highlights, at the joint level, mixed-load conditions due to high dynamic movements and external working forces. Moreover, such systems have a dynamic coupling between the axes due to their mechanical configuration. This mixed-load condition makes the servo-axes design, whose result is the selection of the couple power drive system and transmission, not a trivial procedure. This paper proposes an extensive theoretical discussion that leads to a general procedure for the direct design of the servo axes of multi-degree-of-freedom machinery subject to a mixed-load condition and dynamic coupling between the mechanical joints. The proposed procedure starts with identifying the loads required on the actuated joints without distinguishing between the different contributions. Then, in a few steps, the methodology leads to the direct choice of the PDS/transmission units through a single graphical representation where the load’s peak, thermal and speed conditions are highlighted, along with the possible PDSs and transmissions. The graphical representation proposed also allows the easy and efficient analysis of the effect of transmission selection on the torque and speed margins. Finally, the paper presents the effectiveness of the proposed procedure, applied to the design of the servo axes of a linear delta robot.

Modal Kinematic Analysis of a Parallel Kinematic Robot with Low-Stiffness Transmissions

Several industrial robotic applications that require high speed or high stiffness-to-inertia ratios use parallel kinematic robots. In the cases where the critical point of the application is the speed, the compliance of the main mechanical transmissions placed between the actuators and the parallel kinematic structure can be significantly higher than that of the parallel kinematic structure itself. This paper deals with this kind of system, where the overall performance depends on the maximum speed and on the dynamic behavior. Our research proposes a new approach for the investigation of the modes of vibration of the end-effector placed on the robot structure for a system where the transmission’s compliance is not negligible in relation to the flexibility of the parallel kinematic structure. The approach considers the kinematic and dynamic coupling due to the parallel kinematic structure, the system’s mass distribution and the transmission’s stiffness. In the literature, several papers deal with the dynamic vibration analysis of parallel robots. Some of these also consider the transmissions between the motors and the actuated joints. However, these works mainly deal with the modal analysis of the robot’s mechanical structure or the displacement analysis of the transmission’s effects on the positioning error of the end-effector. The discussion of the proposed approach takes into consideration a linear delta robot. The results show that the system’s natural frequencies and the directions of the end-effector’s modal displacements strongly depend on its position in the working space.

Application and research of robot sorting system based on LabVIEW

Sorting robot is a kind of artificial intelligence robot which has certain sense ability and can classify items. In the sorting industry, its appearance not only reduces the labor input, but also improves the production efficiency of the sorting industry. In this paper, a production line composed of linear Delta robot and 3-DOF robot is studied. The forward and inverse solutions are calculated by MATLAB and simulated by Solid Works. Through the visual processing function, communication function and axle card driving function of Lab VIEW software, the servo motor rotation is controlled to achieve the purpose of the end moving along the predetermined trajectory, and finally the visual sorting function is realized.

An energy-efficient approach for 3D printing with a Linear Delta Robot equipped with optimal springs

In this paper a novel approach for sustainable 3D printing with a Linear Delta Robot equipped with elastic elements is presented and experimentally validated. Energy saving is achieved thanks to the introduction and optimization of linear springs that are mounted on the robot with different configurations: in parallel to the prismatic joints, or directly connecting the end-effector to the fixed frame. The elastic elements allow for a conversion between potential and kinetic energy during a cyclic motion, as for instance the printing of a material layer in additive manufacturing, resulting in actuators energy saving. To reduce the energy consumption, the spring parameters are optimized for the different scenarios by considering the kinematic, dynamic and electro-mechanical models of the parallel robot performing a 3D printing trajectory. The proposed approach is experimentally validated, showing an energy reduction up to almost 50% with respect to the nominal case without springs. The method is general and can be applied for energy efficiency and sustainability in several fields of robotics and computer-integrated manufacturing.

Development of A Linear Delta Robot with Three Horizontal-Axial Pneumatic Actuators for 3-DOF Trajectory Tracking

This paper focuses on developing a pneumatic-driven and horizontal-structure linear delta robot (PH-LDR) and increasing its trajectory tracking performance on the three-degrees-of-freedom (3-DOF) space. With the investigation of inverse and forward kinematics, the parallel mechanism of PH-LDR is designed by using three high-power and low-cost rod-less pneumatic actuators (PAs) to track 3-DOF motion, and this has a horizontal structure to enlarge the workspace. Since the PH-LDR features nonlinear coupling among its three axes and is disturbed by the three high-nonlinear rod-less PAs, the tracking control performance is significantly decreased, subject to uncertain nonlinearity and parametric uncertainty. Therefore, a fuzzy-PID controller is used to achieve highly accurate 3-DOF trajectory tracking, and furthermore, this study exploits neural networks (NNs) to pre-compensate the impacts arising from the compressibility of air and temperature change. The control system for the PH-LDR also features an embedded controller that allows real-time control. Experimental demonstration verifies the developed PH-LDR with the proposed controller, and the dynamic tracking accuracy in 3-DOF trajectory can be achieved.

Пространственный синтез линейного дельта-робота с параллельной кинематикой

Пространственный синтез линейного дельта-робота с параллельной кинематикой

A novel spherical fuzzy QFD method and its application to the linear delta robot technology development

Extensions of ordinary fuzzy sets have been put forward one after the other in the literature. The latest extension is spherical fuzzy sets theory proposed by Kutlu Gündoğdu and Kahraman (2019a), which is based on three independent membership parameters defined on a unit sphere with a constraint related to their squared summation. This new extension presenting larger domains for each parameter is employed for production design in this paper. Quality Function Deployment (QFD) is a structured approach for defining customer needs or requirements, which translates them into the final product in order to satisfy these needs. Spherical fuzzy QFD (SF-QFD) under impreciness and vagueness involving linguistic evaluations rather than exact numerical values is proposed in this paper. The importance ratings and global weights of customer requirements (CR) and improvement directions of design requirements (DR) are successfully represented by using spherical fuzzy sets. Judgments of multi-customers/experts are aggregated by spherical fuzzy aggregation operators. A comparative analysis using SF-TOPSIS is applied for competitive firms. A linear delta robot technology design and evaluation is performed by the proposed SF-QFD and a competitive analysis is presented.

Design and dimensional synthesis of a Linear Delta robot with single legs for additive manufacturing

Parallel manipulator robots are widely used in a large number of applications because they provide important advantages in terms of superior speeds and accelerations, high stiffness and good dynamic performance. In additive manufacturing (AM), this kind of kinematic structures is being increasingly explored to develop new curved and multi-directional fabrication strategies. Based on this application, this work presents the design and dimensional synthesis of a new structure of the Linear Delta parallel robot for AM (3D printing). The new structure uses an innovative concept of Delta mechanism with single legs and rotational joints, which consists of twelve links (three parallel single legs), three prismatic joints and eleven revolute joints. A particular feature of the proposed mechanism is that it contains a joint common to all the kinematic chains instead of a mobile platform as in the conventional Linear Delta structures. Mobility analysis, inverse and direct kinematics, and a study of dimensional synthesis are described in detail. A method of efficient optimization based on genetic algorithms is used to find the minimum dimensional parameters of the robot, considering the maximization of the useful workspace as the main performance index. In order to validate the proposal, a prototype of the robot was built. Capability and geometric deviations analysis was carried out for three test parts resulting in a 0.3-mm deviation/error within a confidence interval of 99.7%.

Kinematics and orientation capability of a family of 3-DOF parallel mechanisms

Existing research demonstrates that the linear Delta robot and the 3-PRS parallel manipulator are different from each other. In this paper, by changing the dimensional parameters of the 4S mechanism in the limb of linear Delta, 35 combinations with the same topology are obtained. The linear Delta and the equivalent 3-PRS parallel manipulator are included in these mechanisms. The unified kinematic model of these 35 mechanisms is established and their possible kinematic characteristics are analyzed as well. According to the constraint requirements of input, the coupling relationship just between the six output parameters of these 35 mechanisms is derived. In addition, the sufficient and necessary conditions for the Delta mechanism to achieve translational motion are demonstrated from the perspective of geometry. By changing dimensional parameters of the 4S mechanism in the chain, its influence on the orientation capability is studied. The coupling relationship just between the six output parameters of the 3-PRS or 3-PSR parallel mechanisms can be easily revealed by the unified kinematic model and the constraint equations. The relationship between the orientation capability and the dimensional parameters indicates that the dimensional parameters can affect the output kinematic characteristics which is not a singularity.

Conceptual design and dimensional optimization of the linear delta robot with single legs for additive manufacturing

Because of remarkable characteristics such as superior speeds and accelerations, high stiffness and good dynamic performance, parallel robots are being increasingly adjusted to different task requirements in the manufacturing field. Their parallel structures made by closed-loop kinematic chains are better suited to develop new curved and multidirectional fabrication strategies in Additive Manufacturing. Based on this application, the conceptual design and dimensional optimization of a new structure of the linear delta parallel robot for Additive Manufacturing (three-dimensional printing) is presented. The new structure uses an innovative concept of delta mechanism with single legs and rotational joints, which consists of 12 links (three single parallel legs), three prismatic joints, and 11 revolute joints. A particular feature of the proposed mechanism is that it contains a joint common to all the kinematic chains instead of a mobile platform. Quality function deployment is used as a methodology for conceptual design. Then the kinematics of the mechanism is described in detail, including mobility analysis, inverse and direct kinematics, and a study of dimensional optimization. A method of efficient optimization based on genetic algorithms is used to find the minimum dimensional parameters of the robot, considering the maximization of the useful workspace as main performance index. Finally, a prototype of the robot is developed to validate the design concepts and functionality of the machine.

Unified Kinematics of Prismatically Actuated Parallel Delta Robots

SummaryThis paper presents a unified formulation for the kinematics, singularity and workspace analyses of parallel delta robots with prismatic actuation. Unlike the existing studies, the derivations presented in this paper are made by assuming variable angles and variable link lengths. Thus, the presented scheme can be used for all of the possible linear delta robot configurations including the ones with asymmetric kinematic chains. Referring to a geometry-based derivation, the paper first formulates the position and the velocity kinematics of linear delta robots with non-iterative exact solutions. Then, all of the singular configurations are identified assuming a parametric content for the Jacobian matrix derived in the velocity kinematics section. Furthermore, a benchmark study is carried out to determine the linear delta robot configuration with the maximum cubic workspace among symmetric and semi-symmetric kinematic chains. In order to show the validity of the proposed approach, two sets of experiments are made, respectively, on the horizontal and the Keops type of linear delta robots. The experiment results for the confirmation of the presented kinematic analysis and the simulation results for the determination of the maximum cubic workspace illustrate the efficacy and the flexible applicability of the proposed framework.

Global Indices for Kinematic and Force Transmission Performance in Parallel Robots

This paper defines, develops, and demonstrates new indices for quantifying kinematic and force transmission performance of parallel robotic mechanisms. Conventional indices are first analyzed and shown to be insufficient for characterizing common design specifications based on worst-case performance. New indices are then developed, analyzed, and extended to simply and intuitively quantify global worst-case kinematic and force performance. These new tools are then successfully applied to the design, optimization, and analysis of a linear delta robot for medical applications.

A μP-μC-FPGA Synergy Controller for a Linear Delta Robot

The paper proposes a novel of fully integrated microprocessor (μP), microcontroller (μC) and field programmable gate array (FPGA) robot controller that combines their processing power to fully control all functions of a linear Delta robot. The μP computes the heavy floating point Mathematics including the control law and all robot kinematics at 1 kHz rate while FPGA processes all digital signals from/to the digital sensors and actuators in parallel. At the same time, the μC interfaces with analog I/O and personal computer and passes the signals to the μP via FPGA. The proposed controller is effectively used to control a robot. The experimental results demonstrate the performance of the proposed controller.

Modelling and Kinematic Analysis of a Built Up Linear Delta Robot

In this paper kinematic analysis of a 3-PUU translational parallel manipulator (TPM) is made by creating the forward and inverse Kinematic solutions. For a given position, control of the end effecter is then realized by using the calculated inverse kinematic parameters as reference values. For kinematic analysis relevant equations are derived from geometrical vector relations. For the forward and inverse kinematic solutions of the non-linear model a MATLAB based iterative algorithm is developed and the inverse kinematic solutions of limbs, are then used to control the end effecter position through screw rails which are driven by DC motors. After the general mechanical design of the manipulator all parts are drawn and modelled in SolidWorks, and a simulation of the motion in three dimensional space is made. To support the reliability of calculated parameters through inverse kinematic solutions, results are compared with the values of SolidWorks based simulation model of the manipulator. Furthermore a real position control with use of feed back encoders is applied and the evaluated results are compared with the results of a simulation model. Very similar and satisfactory results are obtained with both simulation and real application.

Constraint Singularities of Force Transmission in Nonredundant Parallel Robots With Less Than Six Degrees of Freedom

The analysis of the workspace singularities is one of the fundamental aspects in the design of parallel robots. The architecture singularities are generally studied analysing the local properties of the Jacobian matrix. Nevertheless, for limited-DOF parallel robots, there is a category of singularities (constraint or constructive singularities), relating to the constraint force transmission, which are not described by this matrix. This paper deals with a general approach to the analysis of these singularities, used in the synthesis of a Linear Delta robot to suitably modify its geometry, remarkably improving the structural behavior. Details and numerical results are provided.

Optimal Kinematic Design of Spatial Parallel Manipulators: Application to Linear Delta Robot

An optimal kinematic design method suited for parallel manipulators is developed. The kinematic optimization process yields a design that delivers the best compromise between manipulability and a new performance index, space utilization. It is shown that the exhaustive search minimization algorithm is effective for as many as four independent design variables and presents a viable alternative to advanced nonlinear programming methods. The proposed kinematic optimization method is applied to the Linear Delta: a three degree of freedom translational manipulator. The kinematics of the Linear Delta are solved via the polynomial method. The mobility, workspace and manipulability characteristics are examined. It is shown that the Linear Delta’s manipulability generally exhibits relatively little variation when compared to space utilization. The tendency exists for the solution to converge on a zero workspace size architecture when manipulability is optimized alone. The inclusion of the space utilization index in the cost function is crucial for obtaining realistic design candidates.