This paper presents an implementation of the inverse kinematics (IK) solution for an industrial robot based on Conformal Geometric Algebra where the correct signs of the joint angles are extracted using the multivector coefficients and applying the forward kinematics. The solution presented is twice as fast as traditional IK algorithms implemented using matrix algebra, and more than 45 times faster than the IK provided by the robot manufacturer. The proposed solution has been successfully demonstrated and benchmarked in a 3-DOF motion compensation experiment. In addition to being efficient the presented solution requires less matrix operations than for the traditional IK.

In this paper mathematical modelling of a vehicle crash test based on a single mass is studied. The models under consideration consist of a single mass, a spring and/or a damper. They are constructed according to the measured vehicle speed before the collision and measured vehicle accelerations in three directions at the centre of gravity. A new model of nonlinear spring-mass-damper is also proposed to describe the crash.Simulation results are provided to show the effectiveness and applicability of the proposed methods.

Directional control valves play a large role in most hydraulic systems. When modeling the hydraulic systems, it is important that both the steady state and dynamic characteristics of the valves are modeled correctly to reproduce the dynamic characteristics of the entire system. In this paper, a proportional valve (Brevini HPV 41) is investigated to identify its dynamic and steady state characteristics. The steady state characteristics are identified by experimental flow curves. The dynamics are determined through frequency response analysis and identified using several transfer functions. The paper also presents a simulation model of the valve describing both steady state and dynamic characteristics. The simulation results are verified through several experiments.

In this paper mathematical modeling of a vehicle crash test based on a single-mass is studied. The model under consideration consists of a single-mass coupled with a spring and/or a damper. The parameters for the spring and damper are obtained by analyzing the measured acceleration in the center of gravity of the vehicle during a crash. A model with a nonlinear spring and damper is also proposed and the parameters will be optimized with different damper and spring characteristics and optimization algorithms. The optimization algorithms used are interior-point and firefly algorithm. The objective of this paper is to compare different methods used to establish a simple model of a car crash and validate the results against real crash data.

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