This article presents a mathematical analysis of the geometric continuity of industrial robot trajectories, highlighting the influence of continuity conditions on velocity, acceleration, and vibration profiles. This study proposes an original approach: isolating geometric continuity as an independent parameter and the comparative evaluation of the continuity levels C¹, C², and C³ using a series of pre-computed kinematic metrics: vibration energy, acceleration variability, and trajectory curvature stability. The methodology is validated by numerical simulations performed with RoboDK for trajectory generation and by post-processing in Python for metric evaluation. The results indicate that C¹ trajectories exhibit discontinuities in the higher-order derivatives, which lead to undesirable kinematic behaviors, while C² continuity represents the minimum requirement for an acceptable, stable motion in industrial applications. Higher-order continuity, C³, brings greater regularity to the trajectories, but the practical advantages are limited and relatively insignificant for standard industrial applications.

This paper presents the design and development of four educational platforms intended to support industrial logistics students in understanding industrial data acquisition concepts and technologies, using data acquisition and control principles from real industrial applications. To differentiate from other platforms, several features were combined: use of industrial grade automation devices and engineering software environment, while focusing on the monitoring part of an automation system by using data acquisition (DAQ) modules rather than PLCs. A common hardware infrastructure was implemented for all platforms, consisting of a multifunctional printed circuit board (PCB) and a unified communication solution for interfacing with a computer. For each platform, different industrial data acquisition and control modules were used, depending on the types of sensors and actuators. A modular software framework was developed using LabVIEW, enabling the creation of dedicated applications tailored to the educational objectives of each system. The resulting platforms have been implemented in a laboratory in POLITEHNICA Bucharest University, obtaining small-scale industrial monitoring and control systems, for third-year students from Industrial Logistics.