SUMMARY This paper presents a novel method for modeling a 3-degree of freedom open kinematic chain using quaternions algebra and neural network to solve the inverse kinematic problem. The structure of the network was composed of 3 hidden layers with 25 neurons per layer and 1 output layer. The network was trained using the Bayesian regularization backpropagation. The inverse kinematic problem was modeled as a system of six nonlinear equations and six unknowns. Finally, both models were tested using a straight path to compare the results between the Newton–Raphson method and the network training.

This paper presents the modeling of the inverse kinematic problem related to the motions of a delta planar robot using the algebra of unitary Quaternions. The mathematical model resulting from the inverse kinematic analysis has an associated system of 8 nonlinear algebraic equations with 8 polynomial unknowns. The Newton-Raphson method was used to solve the mathematical model of the robot. Subsequently, using the inverse model of the robot, a database was constructed that relates the Cartesian coordinates of the end effector to the angles and axes of the rotations of the links. This database was used to train a multilayer neural network in order to have an equivalent model of the inverse problem. A series of experiments were performed to obtain an improved network configuration by varying four training parameters. The results obtained show that the improved trained network can be used to solve the inverse problem of the studied robot.

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Additive manufacturing has been successfully used as a new technology to produce complex components with improved properties compared with the traditional manufacturing process. However, the powder used as feedstock requires a homogeneous powder mass flow. Velocity and amount of powders fed into the molten pool are crucial to obtain reproducible deposits (tracks). Therefore, monitoring of key parameters in the laser metal deposition (LMD) process is of high importance to obtain repeatability during either repair or printing components. In order to evaluate LMD relevant parameters, a new particle velocity measurement algorithm is proposed. The experimental tests were digitized with a high-speed camera at 8 kHz. Spherical powder of maraging steel with a close size distribution of 90–150 μm has been used as powder feedstock. The algorithm is composed of three modules: the preprocessing of the images, the calculation of the displacement vectors, and the validation and adjustment of the speeds. The sensitivity of the algorithm was validated using synthetic images, showing good performance at noise rates close to 40 dbW. The uncertainty obtained is 0.62m/s, which was calculated by comparing the results obtained against numerical simulations. The proposed method is specific to additive manufacturing processes using metallic powders as feedstock.