Implementation and use of the Levenberg-Marquard algorithm in the problems of calibration of robotic manipulators

The well-known problem of calibration of an arbitrary robotic manipulator, which is formulated in the most general form, is considered. To solve the direct problem of kinematics, an alternative to the Denavit-Hartenberg method, a universal analytical description of the kinematic scheme, taking into account possible errors in the manufacture and assembly of robot parts, is proposed. At the same time, a universal description of the errors in the orientation of the axes of the articulated joints of the links is proposed. On the basis of such a description, the direct and inverse problem of kinematics of robots as spatial mechanisms can be solved, taking into account the distortions of dimensions, the position of the axes of the joints and the positions of the zeros of the angles of their rotation. The problem of calibration of manipulators is formulated as a problem of the least squares method. Analytical formulas of the objective function of the least squares method for solving the problem are obtained. Expressions for the gradient vector and the Hessian of the objective function for the direct algorithm, Newton-Gauss and Levenberg-Marquardt algorithms are obtained by analytical differentiation using a special computer algebra system KiDyM. The procedures in the C ++ language for calculating the elements of the gradient and hessian are automatically generated. On the example of a projected angular 6-degree robot-manipulator, the results of modeling the solution to the problem of its calibration, that is, determination of 36 unknown angular and linear errors, are presented. A comparison is made of the solution of the calibration problem for simulated 64 and 729 experiments, in which the generalized coordinates - the angles in the joints took the values ±90° and -90°, 0, +90°.

Kinematic and dynamic analysis and distribution of stress for seven-item mechanism by means of the SolidWorks program

This paper presents a kinematic and dynamic analysis and distribution of the stress for seven-item planar mechanism by means of the SolidWorks software. The authors of the introduced paper deal with the kinematic analysis of planar mechanisms as well as with the implementation of the vector method into the SolidWorks software program in order to determine the kinematic variables (quantities) of the individual bodies in the whole complex system. The dynamic analysis is performed on the basis of the kinematic analysis. Dynamic analysis allows us to design a system of bodies correctly and it is with the respect to the dynamic loading. For the interpretation of the introduced analysis, the seven-item planar mechanism was selected. Graphic dependence of kinematic and dynamic magnitudes of some points is given in dependence on the angle of rotation of the driving item and in dependence on time. In relation to the kinematic and dynamic analysis and subsequent simulation of the planar as well as spatial mechanisms, it is perfect solution to use SolidWorks software program. The considerable advantage of this mentioned program is based on its simplicity from the aspect of modeling and moreover, it is important to point out that utilisation of the mentioned program leads to results which are precise and accurate in the case of the numerical solution of the equations in the whole magnitude referring to motion of mechanism while the given results are obtained in the graphic form.

Kinematic and dynamic analysis and distribution of stress for six-item mechanism by means of the SolidWorks program

This paper presents a kinematic and dynamic analysis and distribution of the stress for six-item planar mechanism by means of the SolidWorks software. The main purpose of the investigation is connected with the kinematic analysis of planar mechanisms as well as with the implementation of the vector method into the SolidWorks software program in order to determine the kinematic variables of the individual bodies in the whole investigated system. The process of the dynamic analysis is based on the kinematic analysis. The dynamic analysis makes possible to design a system of bodies correctly and it is with the respect to the dynamic loading. For the interpretation of the introduced analysis, the six-item planar mechanism was used as example (representative). Graphic dependence of kinematic and dynamic magnitudes of some points is given in dependence on the angle of rotation of the driving item and in dependence on time. In relation to the kinematic and dynamic analysis and subsequent simulation of the planar as well as spatial mechanisms, it is great solution to use SolidWorks software program. The considerable advantage of this mentioned program is based on its simplicity from the aspect of modeling and moreover, it is important to point out that utilisation of the mentioned program leads to results which are precise and accurate in the case of the numerical solution of the equations in the whole magnitude referring to motion of mechanism while the given results are obtained in the graphic form.

Structural Analysis of the Rhombic Mechanism with an Advanced Connecting Rod of the Working Group of the Stirling Engine

Designing the mechanisms of modern machines is a complex process, where the stage of structural analysis is a priority. When there are a plenty of redundant links in mechanisms their load capacity and efficiency are reduced, increasing the requirements for the accuracy of manufacturing and assembly. It is desirable that mechanisms not requiring high torsional stiffness have no excessive connections; they should be self-aligning. With the advent of new multi-link spatial mechanisms, the task of creating mechanisms without redundant connections becomes more complicated. The structural analysis of the rhombic mechanism of the Stirling engine with a advanced connecting rod of the working group, carried out by the graph method.

A Machine Learning Approach to Solving the Alt-Burmester Problem for Synthesis of Defect-free Spatial Mechanisms

In this paper, we present a machine-learning algorithm to synthesize defect-free single degree of freedom spatial mechanisms for the Alt-Burmester problem. The Alt-Burmester problem is a generalization of a pure motion synthesis problem to include via path-points with missing orientations. While much work has been done towards the synthesis of planar and, to some extent, spherical mechanisms, the generation of mechanisms that are free of circuit, branch, and order defects has proven to be a difficult task. This is even more challenging for spatial mechanisms, which can consist of a large number of circuits and branches. Moreover, the Alt-Burmester problem makes solving such problems using an analytical approach further demanding. In this paper, we present a novel machine-learning algorithm for solving the Alt-Burmester problem for spatial 5-SS platform mechanism using a Variational Auto-Encoder (VAE) architecture. The VAE helps capture the relationship between path and orientation properties of the motion of the 5-SS mechanisms, which enables reformulating the Alt-Burmester problem into a pure motion synthesis problem. The end goal is to produce defect-free spatial mechanism design solutions. While our focus in this paper is on the 5-SS mechanisms, this approach can be scaled to any single-degree-of-freedom spatial mechanisms.

Urban dunes

Sandy shores worldwide suffer from coastal erosion due to a lack of sediment input and sea-level rise. In response, coastal sand nourishments are executed using ‘Building with Nature’ techniques (BwN), in which the sand balance is amplified and natural dynamics are instrumental in the redistribution of sand, cross- and alongshore. These nourishments contribute to the growth of beaches and dunes, serving various design objectives (such as flood safety, nature, and recreation). Nevertheless, human interference (such as buildings and traffic) along urbanized sandy shores may have significant, yet poorly understood, effects on beach and dune development. Better insight is required into the interplay of morphological, ecological and urban processes to support Aeolian BwN processes for dune formation and contribute to the sustainable design of urbanized coastal zones. This paper aims to bridge the gap between coastal engineering and urban design by formulating design principles for BwN along urbanized sandy shores, combining nourishments, natural dune formation and urban development on a local scale to strengthen the coastal buffer. The first part of the paper analyses sedimentation processes in the (built) sea-land interface and identifies spatial mechanisms that relate coastal occupation to dune formation. Hence a preliminary set of design principles is derived by manipulating wind-driven sediment transport for BwN dune formation after nourishment. In the second part of the paper, these principles are applied and contextualized in two case-studies to compare their capability for BwN in different coastal profiles: the vast, rural, geomorphologically high dynamic profile of a mega-nourishment (Sand Motor); versus the compact, highly urbanized, profile(s) of a coastal resort (Noordwijk). Conclusions reflect on the applicability of BwN design principles within different coastal settings (dynamics, urbanity) and spatial arrangements facilitating BwN dune formation.

Variable degree-of-freedom spatial mechanisms composed of four circular translation joints

This paper deals with the construction and reconfiguration analysis of a spatial mechanism composed of four circular translation (G) joints. Two links connected by a G joint, which can be in different forms such as a planar parallelogram, translate along a circular trajectory with respect to each other. A spatial 4G mechanism, which is composed of four G joints, usually has 1-DOF (degree-of-freedom). Firstly, a 2-DOF spatial 4G mechanism is constructed. Then a novel variable-DOF spatial 4G mechanism is constructed starting from the 2-DOF 4G mechanism using the approach based on screw theory. Finally, the reconfiguration analysis is carried out in the configuration space using dual quaternions and tools from algebraic geometry. The analysis shows that the variable-DOF spatial 4G mechanism has one 2-DOF motion mode and one to two 1-DOF motion modes and reveals how the 4G mechanism can switch among these motion modes. By removing one link from two adjacent G joints each and two links from each of the remaining two G joints, we can obtain a queer-rectangle and a queer-parallelogram, which are the generalization of the queer-square or derivative queer-square in the literature. The approach in this paper can be extended to the analysis of other types of coupled mechanisms using cables and gears and multi-mode spatial mechanisms involving G joints.