For control applications, the angular velocity of the drive crank of a four-bar mechanism is traditionally assumed to be constant. In this paper, we propose control of variable velocity of the drive crank to obtain the desired output motions for the coupler point. To estimate the reference trajectory for the crank velocity, a neural network is trained with data from the kinematic model. The control law is designed from feedback linearization of the tracking error dynamics and a Proportional–Integral–Derivative (PID) controller. The applicability of the proposed scheme is validated through simulations for three variable speed profiles, obtaining excellent results from the system.

Earth observation with unmanned aerial vehicles (UAVs) offers an extraordinary opportunity to bridge the gap between field observations and traditional air and space-borne remote sensing. In this regard, ground landing stations (GLS) systems play a central role to increase the time and area coverage of UAV missions. Bluetooth low energy (BLE) technology and the received signal strength indicator (RSSI) techniques have been proposed for target location during UAV landing. However, these RSSI-based techniques present a lack of precision due to the propagation medium characteristics, which leads to UAV position vagueness. In this sense, the development of a novel low-cost GLS system for UAV tracking and landing is proposed. The GLS system has been embodied for the purpose of testing the UAV landing navigation capability. The maximum likelihood estimator (MLE) algorithm is addressed on an embedded microcontroller for the position estimation based on the RSSI acquired from an array of BLE devices. Experimental results demonstrate the feasibility and accuracy of the ground landing station system, achieving average errors of less than 0.04 m with the UAV-MLE target position estimation approach. This 0.04 m distance represents an order of magnitude increase in location precision over other currently available solutions. In many cases, this increased precision can enable more innovative docking mechanisms, less likelihood of mishaps in docking, and also quicker docking. It may also facilitate docking procedures where the docking station is itself moving, which may be the case if the docking unit is a mobile ground rover.

We introduce a comprehensive methodology for calculating the propagation of errors in kinematic quantities up to the jerk for robotic systems and mechanical linkages. Our study utilizes two distinct computational approaches: a deterministic method that relies on derivative calculations, and a stochastic method that utilizes Monte Carlo simulations. Kinematic quantities are computed using dual numbers while the variation in the parameters is computed using the complex step approximation method, as well as with the use of dual numbers to include the general case of a function of complex variables. Although the deterministic approach is generally more efficient, the stochastic method stands out for its simplicity and ease of implementation. The efficacy of our methodology is demonstrated through practical applications. We perform error propagation analyses up to the jerk for planar and spherical four-bar (4R) mechanisms and a revolute–cylindrical–revolute (RCR) robot manipulator, highlighting its versatility across different mechanical systems.

Quaternions are used in various applications, especially in those where it is necessary to model and represent rotational movements, both in the plane and in space, such as in the modeling of the movements of robots and mechanisms. In this article, a methodology to model the rigid rotations of coupled bodies by means of unit quaternions is presented. Two parallel robots were modeled: a planar RRR robot and a spatial motion PRRS robot using the proposed methodology. Inverse kinematic problems were formulated for both models. The planar RRR robot model generated a system of 21 nonlinear equations and 18 unknowns and a system of 36 nonlinear equations and 33 unknowns for the case of space robot PRRS; both systems of equations were of the polynomial algebraic type. The systems of equations were solved using the Broyden–Fletcher–Goldfarb–Shanno nonlinear programming algorithm and Mathematica V12 symbolic computation software. The modeling methodology and the algebra of unitary quaternions allowed the systematic study of the movements of both robots and the generation of mathematical models clearly and functionally.

In this paper we propose a numerical solution (software simulation) of the "problem of n bodies" that interact gravitationally based on the formulation of Verlet. Additionally a program is designed that graphically shows the results of this numerical solution, which details the different trajectories, for different conditions of mass, speed and distance between the n objects that interact. The interaction of the user with the graphical interface, is performed particle by particle.

Quaternions are used in various applications, especially in those where it is necessary to model and represent rotational movements, both in the plane and in space, such as in the modeling of the movements of robots and mechanisms. In this article, a methodology to model the rigid rotations of coupled bodies by means of unit quaternions is presented. Two parallel robots were modeled: a planar RRR robot and a spatial motion PRRS robot using the proposed methodology. Inverse kinematic problems were formulated for both models. The planar RRR robot model generated a system of 21 nonlinear equations and 18 unknowns, and a system of 36 nonlinear equations and 33 unknowns for the case of space robot PRRS; both systems of equations were of the polynomial algebraic type. The systems of equations were solved using the Broyden-Fletcher-Goldfarb-Shanno nonlinear programming algorithm and Mathematica V12 symbolic computation software. The modeling methodology and the algebra of unitary quaternions allowed the systematic study of the movements of both robots and the generation of mathematical models clearly and functionally.