Mathematical Analysis and Practical Applications of a Serial-Parallel Robot with Delta-Like Architecture

In the early 1980s, Delta robot was invented by R. Clavel [1]. It is coupled with three axis’ tandem arms at the end of the platform [2-6]. The advantages of designing so is that each single motor shared the loads in parallel mechanical arm so that it can reduce the wattage [7-11]. Moreover, delta robot is a parallel closed chain designed, and thus the overall rigidity of the machine is stronger and the inertia of movements are smaller as well [12-16]. However, besides the favorable advantages, it is actually difficult to have dynamic errors and cumulative errors, which could lead to inaccuracy results for the overall performances.

 Therefore, emphasizing the advantages of serial and parallel institutions while simultaneously maintaining both stabilities and accuracies of the delta robot performances is a critical issue [17, 18] to be concerned. The previous article [17] was focused on the development of mechanism with hybrid kinematic structure called Trivariant. The trajectory can be controlled manually or automatically during the computer simulation. U. Thomas et al. [18] developed a unified notation for serial, parallel, and hybrid kinematic structures. With the extended DH-parameters, users were able to describe spherical, cardan, cylindrical, rotational, and prismatic joints following the well-known intuitive notation. However, only the simulation results were presented to verify the effectiveness. To address the above-mentioned problems, we developed a novel serial-parallel hybrid design of delta robot, which aim to avoid the drawbacks of both the dynamic errors and cumulative ones.

 The design of a modified delta robot can briefly divided into two parts in terms of hardware and software systems. Considering the hardware system, it can be further subdivided into three parts including mechanical design, wiring and assembling. We use the software SolidWorks to design and simulate the overall mechanical structures and its kinematic movements by using large mechanical disassembly techniques. Then, the software system can also be further divided into the kinematic model, motor control, image processing and algorithms in projects. A modular package involving control is developed to speed up the overall computational time. To verify the system, several complex tasks are introduced to challenge the stabilities and reliabilities of the proposed delta robot system, including drawing, playing dominos, and objects classification based on image processing, and so on. 

The remainder of this paper is organized as follows. Section II gives a mathematical analysis of the delta robot. Section III presents the design of both hardware and software systems of the proposed delta robot. Section IV presents the experimental results to verify the performances of the proposed system. Discussions of the proposed delta robot is given in Section V, and the conclusion of this paper is introduced in Section VI.