# A Study on the Errors of 2D Circular Trajectories Generated on a 3D Printer
## 1 Introduction  
The additive fabrication is a common topic in various domains of activity (industry, biology, medicine). The compliance with precision conditions of 3D-printed parts (shape and dimensions tolerances, surface quality, etc.) becomes more and more a critical issue. Their use in some technical applications where precision and accuracy (P&A) are required is severely restricted since, for the present, other manufacturing technologies offer better results. Many studies in engineering and scientific research are focused on ensuring the P&A of 3D printers by error avoidance [1]. Other studies are involved in experimental research (measurements and data processing) in order to verify and to correct the errors generated by the lack of P&A on 3D printers by error compensation [1]. There are many issues involved in the appearance of errors in additive fabrication. Not surprisingly, some of them are not related with the 3D printer features (e.g., structure, P&A of kinematics, dynamics, position control, deposition process, temperature, etc.). For example, in [2] is established that the accuracy of STL (.stl) files (from Standard Tessellation Language or Standard Triangle Language, commonly used by Fused Deposition Modelling on 3D printers) essentially depends on the design of 3D CAD models (six different CAD systems generate STL files with different accuracies). In [3], is established that the conversion in STL format is done with errors by some CAD software products. The software interface used to drive the printer (slicer software, establishing the way the model is built) is often a source of inaccuracy [4] when inappropriate values of setting parameters are suggested by the software and accepted by user [5]. Sometimes the CAD models are generated with errors (and these errors are transferred to the printed object), especially when these models are generated as a virtual copy of areal object, e.g., by imaging, segmentation, and post processing of medical models [6; 7] or by reverse engineering using a 3D-scanning and design process [8; 9]. Some sources of errors are related to material deposition during additive manufacturing (e.g., flow properties) as susceptible to random variations [5]. The effect of print layer height on the accuracy of orthodontic models is considered in [10]. The effect of orientation (effect of gravity) and the effect of the support are investigated by [1]. A study on the influence of the accuracy related to size/position of printed benchmarks and the position of working planes on 3D printers is revealed in [11].The influence on P&A and mechanical properties (measured by tensile test) of a specimen object related to the print position of a specimen object is presented in [12; 13]. The influence of different common printing technologies on the accuracy of mandibular models was considered in the research results shown in [14]. The influence of different types of thermoplastic filament materials used in additive fabrication on surface roughness was evaluated in [15]. The evolution in time of internal material tension, dimension and shape (by aging) as source of errors in 3D printing is a topic studied in [16]. A simple method to appreciate the P&A of 3D printers (and to calibrate it as well) is the measurement of a printed object (the most common being \"#3D Benchy\" from Creative Tools) or the quality of a printed structure (e.g.,\"#All in one test 3D printer\"). In [17], an insitu measurement method (by the scanning of layers) during the additive manufacturing process is proposed. The use of a coordinate measurement machine is proposed to describe the accuracy of medical models in [18; 19]) and the optical scanning is mentioned in [6]). A metrology feedback procedure is used in [20; 21] to improve the geometrical accuracy by errors compensation using a 3D scanning on sacrificial printed objects. The displacement errors and the errors of the relative position of movable parts are often related by kinematics of a 3D printer.