Trajectory-tracking of 6-RSS Stewart-Gough manipulator by feedback-linearization control using a novel inverse dynamic model based on the force distribution algorithm

ABSTRACT

6-RSS Stewart-Gough parallel manipulator contains six crank-rod limbs connecting the base and moving platforms to each other, forming a 6DOF manipulator. In this paper, we introduce a novel decoupled inverse dynamic model for this manipulator based on the Force Distribution Algorithm. The performance of the proposed model was evaluated in tracking a complex trajectory (of multiple segments with simultaneous translational and rotational motions) using feedback-linearization control in the joint space and compared with that of the Lagrangian inverse dynamic model. Results showed that this model leads to a better performance in feedback-linearization control, especially when the reference trajectory is quantized, and with less calculation burden in comparison with the Lagrangian model. The control system employing both models showed robustness against payload uncertainty on the moving platform (150% of the moving platform’s mass). The performance assessment and the robustness approval were performed in simulation using a Simscape model specifically built for this purpose in the Simulink environment.     

A brief history of mathematics education in Turkey: K-12 mathematics curricula

In this study, we survey the history of mathematics education in Turkey starting with its historical roots in the foundation of the republic. The changes in mathematics education in Turkey over the last century are investigated through an analysis of changes in curricular documents for K-12 schools. We consider the factors and reasons affecting curriculum developments, changes in philosophy and structure in terms of standards, objective and instructions. This article utilizes archival research techniques by examining original sources and illustrates the nature of the changes benefiting from a historical perspective. As a result of such analysis of the aforesaid sources, we have seen that the main reasons for changing mathematics curricula are: to build up a modern civilization in Turkey; the reports of John Dewey and the recommendations of Kate Wofford, William C. Varaceus and Watson Dickerman; the desire to become a member of the European Union; international factors and political situations.     

A generalisation of a theorem of Koldunov with an elementary proof

We generalize a Theorem of Koldunov [2] and prove that a disjointness proserving quasi-linear operator between Resz spaces has the Hammerstein property.     

The MTPO/Malyughinetz hybrid method for the scattering analysis of parabolic impedance reflectors

The scattering process of cylindrical waves, radiated by a line source, from a parabolic reflector is investigated with the MTPO/Malyughinetz hybrid method. The geometrical optics and diffracted waves are evaluated asymptotically from the radiation integral. The scattered, diffracted and geometrical optics waves are plotted numerically for different impedance values.     

An infrared and Raman spectroscopic study of Td-type 4,4′-bipyridylcadmium(II) tetracyanometallate (II) benzene (1/2) clathrates: Cd(C10H8N2)Cd(CN)4 · 2C6H6 and Cd(C10H8N2)Hg(CN)4 · 2C6H6

Two new benzene clathrates of the form Cd(4,4-bipyridyl)M(CN)₄ · 2C₆H₆, (M=Cd or Hg) have been prepared in powder form. Their spectral data were compared with those of the corresponding host complexes and found to be consistent with the host structure found in Td-type clathrates.     

Synthesis,Spectrothermal Behaviour and Molecular Structure of Aquaorotatotriethanolaminenickel(II) Monohydrate

The aquaorotatotriethanolaminenickel(II) monohydrate, [Ni(HOr)(H₂O)(tea)]·H₂O ( 1 ), was synthesized and characterized by means of elementel analysis, IR and UV‐Vis, spectroscopy, magnetic susceptibility, thermal analysis and X‐ray diffraction techniques. The nickel ion in [Ni(C₅H₂N₂O₄)(H₂O)(N(C₂H₄OH)₃)] is chelated to the deprotonated N3 pyrimidine atom and to the carboxylate oxygen atom of the bidentate orotate dianion, and to the one nitrogen and two oxygen atoms of the tridentate triethanolamine molecule and its octahedral geometry is completed by an aqua ligand. It crystallizes in the monoclinic system, space group P2₁/c with lattice parameters a = 7.1528(5) Å, b = 19.4903(14) Å, c = 11.8085(8) Å, β = 106.237(5)°, V = 1580.55(19) ų, Z = 4. An extensive three dimensional network of O_w‐H…O, N‐H…O and O‐H…O hydrogen bonds, π‐π and π‐ring interactions are responsible for crystal stabilization. The decomposition reaction take places in the temperature range 20‐1000 °C in the static air atmosphere. Thermal decomposition of 1 proceeds in three stages.     

Fused heterocycles: synthesis of some new imidazo[1,2-a]- pyridine derivatives

Some new thiazolidines and spirothiazolidines derived from hydrazones of 2-methylimidazo[1,2-a]pyridine-3-carboxylic acid hydrazide, a bioisosteric derivative of isoniazid, were synthesized and characterized by analytical, IR, (1)H- and (13)C-NMR and mass spectral data. Some of the newly synthesized compounds were screened for their antimycobacterial activities. None of the tested compounds showed significant in vitro antituberculous activity at 6.25 mirog/mL (MIC rifampin 0.031 microg/mL).     

Spin bath decoherence of quantum entanglement

We study an analytically solvable model for decoherence of a two spin system embedded in a large spin environment. As a measure of entanglement, we evaluate the concurrence for the Bell states (Einstein-Podolsky-Rosen pairs). We find that while for two separate spin baths all four Bell states lose their coherence with the same time dependence, for a common spin bath, two of the states decay faster than the others. We explain this difference by the relative orientation of the individual spins in the pair. We also examine how the Bell inequality is violated in the coherent regime. Both for one bath and two bath cases, we find that while two of the Bell states always obey the inequality, the other two violate the inequality at early times.     

Stability of gas pressure regulators

Gas pressure regulators are widely used in both commercial and residential applications to control the operational pressure of the gas. One common problem in these systems is the tendency for the regulating apparatus to vibrate in an unstable manner during operation. These vibrations tend to cause an auditory hum in the unit, which may cause fatigue damage and failure if left unchecked. This work investigates the stability characteristics of a specific type of hardware and shows the cause of the vibration and possible design modifications that eliminate the unstable vibration modes. A dynamic model of a typical pressure regulator is developed, and a linearized model is then used to investigate the sensitivity of the most important governing parameters. The values of the design parameters are optimized using root locus techniques, and the design trade-offs are discussed.     

Use of polyethylene glycol coatings for optical fibre humidity sensing

Humidity induced change in the refractive index and thickness of the polyethylene glycol (PEG) coatings are in situ investigated for a range from 10 to 95%, using an optical waveguide spectroscopic technique. It is experimentally demonstrated that, upon humidity change, the optical and swelling characteristics of the PEG coatings can be employed to build a plastic fibre optic humidity sensor. The sensing mechanism is based on the humidity induced change in the refractive index of the PEG film, which is directly coated onto a polished segment of a plastic optical fibre with dip-coating method. It is observed that PEG, which is a highly hydrophilic material, shows no monotonic linear response to humidity but gives different characteristics for various ranges of humidity levels both in index of refraction and in thickness. It undergoes a physical phase change from a semi-crystalline structure to a gel one at around 80% relative humidity. At this phase change point, a drastic decrease occurs in the index of refraction as well as a drastic increase in the swelling of the PEG film. In addition, PEG coatings are hydrogenated in a vacuum chamber. It is observed that the hydrogen has a preventing effect on the humidity induced phase change in PEG coatings. Finally, the possibility of using PEG coatings in construction of a real plastic fibre optic humidity sensor is discussed.