“…It is based on inertia matrices [4,11], transformation matrices [1,3,14,17,20], centres of mass position vectors [2,16] and model masses. All of these parameters are taken from the SolidWorks CAD model.…”
Section: Th Daaam International Symposium On Intelligent Manufacturmentioning
confidence: 99%
“…Nowadays, a wide range of different support software tools are available; it provides many possibilities and ways to determine mathematical or physical model [4,5,6,7,9,10,11,13,14,15,17,18,19,20]. Accurate detection of a mathematical model is complicated in the case of a complex mechanical structure with many parts, and it should not be used for simulation purposes and controller determination at the same time.…”
Section: Introductionmentioning
confidence: 99%
“…Accurate detection of a mathematical model is complicated in the case of a complex mechanical structure with many parts, and it should not be used for simulation purposes and controller determination at the same time. The chosen way is to split the problem between 2 models is: the most accurate model for a simulation as a real (physics) model substitution -physical model [4,9,14,18] and appropriately simplified model purely for a controller determination -mathematical model [7,19,20].…”
Dynamic behaviour comparison of three different mathematical descriptions complexity for first 3 joints of 6 degrees of freedom robotic structure is presented in this article. Firstly, 3D CAD model is designed in SolidWorks, which is used as the basis for a physical and mathematical model. The CAD model is exported directly from SolidWorks to SimMechanics as a physical model which is considered as the most accurate replacement for a real model in this work. The first type of a mathematical model is the most precise but also the most complex; it is based on SolidWorks inertia matrices and matrix form of Lagrange's motion equations of the second kind. The second type of a mathematical model is created by each part replacement with a suitable simplified shape; classical integration approach with Lagrange's motion equations of the second kind is used. The third type of a mathematical model is based on the same approach as the second type, but all the objects are replaced by mass points. At the end, all the results of dynamic behaviour are compared with the physical model, for utilization in controller design.
“…It is based on inertia matrices [4,11], transformation matrices [1,3,14,17,20], centres of mass position vectors [2,16] and model masses. All of these parameters are taken from the SolidWorks CAD model.…”
Section: Th Daaam International Symposium On Intelligent Manufacturmentioning
confidence: 99%
“…Nowadays, a wide range of different support software tools are available; it provides many possibilities and ways to determine mathematical or physical model [4,5,6,7,9,10,11,13,14,15,17,18,19,20]. Accurate detection of a mathematical model is complicated in the case of a complex mechanical structure with many parts, and it should not be used for simulation purposes and controller determination at the same time.…”
Section: Introductionmentioning
confidence: 99%
“…Accurate detection of a mathematical model is complicated in the case of a complex mechanical structure with many parts, and it should not be used for simulation purposes and controller determination at the same time. The chosen way is to split the problem between 2 models is: the most accurate model for a simulation as a real (physics) model substitution -physical model [4,9,14,18] and appropriately simplified model purely for a controller determination -mathematical model [7,19,20].…”
Dynamic behaviour comparison of three different mathematical descriptions complexity for first 3 joints of 6 degrees of freedom robotic structure is presented in this article. Firstly, 3D CAD model is designed in SolidWorks, which is used as the basis for a physical and mathematical model. The CAD model is exported directly from SolidWorks to SimMechanics as a physical model which is considered as the most accurate replacement for a real model in this work. The first type of a mathematical model is the most precise but also the most complex; it is based on SolidWorks inertia matrices and matrix form of Lagrange's motion equations of the second kind. The second type of a mathematical model is created by each part replacement with a suitable simplified shape; classical integration approach with Lagrange's motion equations of the second kind is used. The third type of a mathematical model is based on the same approach as the second type, but all the objects are replaced by mass points. At the end, all the results of dynamic behaviour are compared with the physical model, for utilization in controller design.
“…Kinematic and dynamic modeling of robots and mechanisms has been performed by applying various mathematical tools and methodologies. For example, homogeneous matrices and the Denavit-Hartenberg methodology are commonly used to generate mathematical models related to robots 1 and mechanisms, 2 both in plane and in space. Other methods such as the Euler-Rodrigues parameters 3 and quaternions algebra 4 are also considered for modeling of rotations and translations of robots.…”
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.
“…The mathematical model´s outputs or captured laboratory model variables (for virtual animation purposes) are used as 3D Animation model inputs [6,9]. These parameters are converted into the appropriate format by a transformation matrix using Euler parameters [1,3,4].…”
This article introduces the possibilities of the simulation and visualisation of the "Twin-Rotor MIMO System" laboratory model outputs by means of various support software tools. The 3D model of the system, (used for simulation and visualisation), is designed in SolidWorks 3D CAD software. Matlab/Simulink with extension libraries like Simscape and 3D Animation -(formerly Virtual Reality Toolbox), is used for 3D visualisation and simulation. The 3D Animation toolbox is only used for the visualisation of the mathematical and real models. The Simscape library -on the other hand, is used for the validation of the reverse control of the derived mathematical model´s correctness and for simulation and analysis purposes as a suitable substitution for real models. As a result of this, these supporting software tools streamline the overall suggested controls -from analysis to presentation of the results.
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