An Efficient Algorithm for Workspace Generation of Delta Robot

Mechanism and Machine Theory, 2007

This paper deals with an optimal dimensional synthesis method of the DELTA parallel robot for a prescribed workspace. The objective function is based on the mathematical concept of the power of a point with respect to bounding constraint surfaces. A genetic algorithm based method was used to solve this problem. The proposed method is simple and was shown to be effective in finding the dimensions of the DELTA robot having the smallest workspace containing a prespecified region in space. These dimensions were also determined in the case where the user defines a safety region, to avoid points in the prescribed workspace being on the boundary of the DELTA robot's actual workspace.

Parallel Manipulators, towards New Applications, 2008

Mechanism and Machine Theory, 2020

This paper presents an analytical approach for the dimensional synthesis of the 3-DOF Delta parallel robot for a prescribed workspace. The dimensional synthesis of parallel robots is a challenging problem for which obtaining an analytical solution is a cumbersome task and no appropriate analytical closed-form solution has been developed for the DPR so far. First, the workspace is analytically calculated based on inverse kinematic and it showed that the workspace of DPR comes from some geometric conditions. Afterward, the largest possible box which can be inserted in the workspace is obtained. Optimal analytical dimensional design for a prescribed workspace is calculated by considering three types of construction constraints. Optimization objectives based on subjective and the smallest robot criterion have been defined which is optimized by resorting to the so-called Lagrange multiplier method. The results revealed that in the best case of the existing industrial robots, workspace expression is only close to %87.29 of the optimal workspace of this paper and in optimal design it could have up to %51.70 smaller robot with the same given workspace.

In this paper, a new design method considering a desired workspace and swing range of spherical joints of a DELTA robot is presented. The design is based on a new concept, which is the maximum inscribed workspace proposed in this paper. Firstly, the geometric description of the workspace for a DELTA robot is discussed, especially, the concept of the maximum inscribed workspace for the robot is proposed. The inscribed radius of the workspace on a workspace section is illustrated. As an applying example, a design result of the DELTA robot with a given workspace is presented and the reasonability is checked with the conditioning index. The results of the paper are very useful for the design and application of the parallel robot.

In this paper, a new design method considering a desired workspace and swing range of spherical joints of a DELTA robot is presented. The design is based on a new concept, which is the maximum inscribed workspace proposed in this paper. Firstly, the geometric description of the workspace for a DELTA robot is discussed, especially, the concept of the maximum inscribed workspace for the robot is proposed. The inscribed radius of the workspace on a workspace section is illustrated. As an applying example, a design result of the DELTA robot with a given workspace is presented and the reasonability is checked with the conditioning index. The results of the paper are very useful for the design and application of the parallel robot.

2013 IEEE International Conference on Robotics and Biomimetics (ROBIO), 2013

In their search for perfection and competitiveness, Colombian industrial concerns now see in robotics a viable way to improve their processes. On such ground, this paper proposes design methodology of a parallel Delta-type industrial robot. This type of robot is an alternative for Colombian industries, since its great advantages of Speed, Precision, and Accuracy make it usable in product packing and selection. The prototype made will allow future applications in the regional industry, guaranteeing a suitable process automation alternative.

2008 7th World Congress on Intelligent Control and Automation, 2008

Determine an optimal set of design parameter of PR whose DW fits a prescribed workspace as closely as possible is an important and foremost design task before manufacturing. In this paper, an optimal design method of a linear Delta robot (LDR) to obtain the prescribed cuboid dexterous workspace (PCDW) is proposed. The optical algorithms are based on the concept of performance chart. The performance chart shows the relationship between a criterion and design parameters graphically and globally. The kinematic problem is analyzed in brief to determine the design parameters and their relation. Two algorithms are designed to determine the maximal inscribed rectangle of dexterous workspace in the O-xy plane and plot the performance chart. As an applying example, a design result of the LDR with a prescribed cuboid dexterous workspace is presented. The optical results shown that every corresponding maximal inscribed rectangle can be obtained for every given RATE by the algorithm and the error of RATE is less than 0.05.The method and the results of this paper are very useful for the design and comparison of the parallel robot.

Mechanism and Machine Theory, 2018

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Journal of Mechanical Design, 2003

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.

Proceedings of IEEE International Conference on Robotics and Automation, 1996

We present a method for designing optimal parallel manipulators of the Gough platform type, according to design constraints like a specified workspace, best accuracy over the workspace, minimum articular forces for a given load, etc .... A reduced set of design parameters is defined and the workspace constraints are used to compute the zone of the parameters space which define all the robots whose workspace include the desired workspace. Then a numerical search is performed in this zone to determine the robot which optimize some other criterion. We show how the method has been used to design a robot whose accuracy was specified to be better than 1 l m for a nominal load of 500 kg.