Dear Colleagues,

Applied mechanics in robotics refers to the modeling and simulation of the geometry, kinematics, elastokinematics, dynamics, and elastodynamics of the rigid or elastic structures of robots.

This analysis is performed on robots characterized by serial and parallel structures, as well as on mobile robots. The study of geometry and kinematics is based on the forward and inverse (control) model, respectively. New formulations in geometry and kinematics are based, on the one hand, on homogeneous transformations and, on the other hand, on the use of matrix exponentials and of quaternions. In the case of fast movements, impulsive movements, and the movements in transient regimes, the study of advanced kinematics and elastokinematics involves the use of higher-order accelerations and polynomial interpolation functions of a higher order.

New formulations in dynamic and elastodynamic modeling are based on the differential principle from analytical mechanics, which is specific to rigid structures (Lagrange equations of the second kind, Hamilton equations, Appell equations, and the Gauss principle), as well as on principles from the elasticity theorem. As robots are characterized by rapid movements, the study of advanced dynamics will be extended, using as central functions the acceleration energies of a higher order, which will lead to a generalization of the D'Alembert–Lagrange differential principle. As a consequence, the determination of the differential equations of a higher order that are defining will also pose a problem; from the dynamic point of view, these comprise the fast and transient movements of robot structures. A relevant aspect of this study is the dynamic inverse modeling by which the time variation laws of the driving moments (torques) corresponding to each driving joint from the robot structure are determined. This dynamic and elastodynamic study will be carried out by taking into account different types of friction that can develop within the mechanical structure of the robot. Other important issues that will be dealt with in this Special Issue are represented by problems regarding the optimization of motion trajectories for different robot structures, and by problems related to the accuracy and modeling of trajectory errors.

The main purpose of this Special Issue is to encourage researchers to share the latest developments in the field of advanced dynamics of robotic systems; higher-order dynamic equations; analytical dynamics of complex systems; and mathematical modelling of serial, parallel, and mobile robot structures (e.g., the use of matrix exponential or of polynomial interpolation functions and the establishment of dynamic equations of motion based on the acceleration energies).

Prof. Dr. Iuliu Negrean
Guest Editor

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• Robotics
• Kinematics control
• Advanced kinematics
• Matrix exponentials in robotics
• Motion trajectories
• Robot dynamics
• Acceleration energies
• Analytical dynamics
• Advanced dynamics