Synthesis of the forward kinematics problem algebraic modeling for the general parallel manipulator: displacement-based equations

This paper closes a triptic to address the issue of the forward kinematics problem (FKP) aimed at certified solving with an exact algebraic method. This solving method was described in the first article published in Advanced Robotics. The second one investigated the formulation specifically applied to the planar parallel manipulators. This third paper is the logical one in the footsteps of the formersones, since it continues the formulation analyses and brings them to the general spatial parallel manipulator. Hence, this paper focuses on the displacement-based equation systems. This paper is the first one to present a synthesis on forward kinematics modeling focusing on finding an optimal mathematical formulation based on the displacement-based equation systems. The majority of parallel manipulators in applications can be modeled by the 6-6 hexapod or so-called Gough platform which is constituted by a fixed base and a mobile platform attached to six kinematics chains with linear (prismatic) actuators located between two revolute or Cardan joints. Again, in order to implement algebraic methods, the parallel manipulator kinematics shall be formulated as polynomial equations systems where the equation number is at least equal to the unknown numbers. Six geometric formulations were derived. The selected algebraic proven method is implementing Gröbner bases from which it constructs an equivalent univariate polynomial system. The resolution of this last system exactly determines the real solutions which correspond to the manipulator postures. The FKP resolution of the general 6-6 parallel manipulator outputs 40 complex solutions. Several instantiations shall be computed in order to select the model which leads to the FKP resolution with the lowest response times and smaller file sizes. It was possible to reject three modelings leading to bad performances or resolution failure. It was possible to determine one formulation where the solving computations were definitely better than the others.     

用REAL流媒体技术回传电台直播信号初探

随着互联网接入技术和计算机多媒体技术的发展，流媒体技术得到了飞速发展并广泛应用。本文着重介绍了流媒体技术和我局应用REAL流媒体技术回传电台直播信号的实践经验。     

Certified solving of the forward kinematics problem with an exact algebraic method for the general parallel manipulator

This article introduces an exact method to solve the forward kinematics problem (FKP) specifically applied to spatial parallel manipulators. The majority can modeled by the 6-6 parallel manipulator. This manipulator is a hexapod made up of a fixed base and a mobile platform attached to six kinematics chains with linear (prismatic) actuators located between two ball or Cardan joints. In order to implement algebraic methods, the parallel manipulator kinematics will be formulated as polynomial equations systems where the equation number is equal to the unknown numbers. One position-based kinematics model will be identified to solve the difficult FKP. The selected proven algebraic method implements Gröbner bases and constructs an equivalent univariate polynomial system. The exact resolution of this last system determines the real solution which exactly corresponds to the manipulator postures. The FKP resolution of the general 6-6 parallel manipulator outputs 40 complex solutions. We provide several examples of various hexapod types yielding eight real solutions. This algebraic method is exact and computes certified results.     

Optimisation of work roll shifting and bending to roll thinner gauge HR coils using genetic algorithm

Abstract

Rolling of thin gauge hot rolled (HR) coils demands stringent flatness tolerance. Thin HR coils (≤3 mm) are rolled towards the end of any rolling campaign. The profile and flatness of the strip depend on the profile of the loaded roll gap in the mill stands. There are five key factors that influence the loaded roll gap: initial roll surface profile, roll thermal expansion, wear of roll, deflection of roll stack and shifting of work rolls. This paper deals with all these factors individually for the formulation of an objective function in order to minimise the flatness error. The shifting and bending of rolls are the controllable parameters that require optimising. This has been accomplished using a genetic algorithm (GA) optimisation technique.     

In situ observation of solidification phenomena in Al–Cu and Fe–Si–Al alloys

Abstract

Synchrotron radiation enables the observation of solidification in metallic alloys. In situ observations of solidification for Al–Cu alloys (5, 10 and 15 wt-%Cu) are reported. Nucleation and fragmentation of dendrite arms were often observed in the 15 and 10%Cu alloys when unidirectional solidification was performed from the planar interface. In contrast, nucleation and fragmentation were rarely observed in the 5%Cu alloys. The nucleation ahead of the solidifying front and the fragmentation in the mushy region strongly depended on alloy composition. This paper also presents in situ observation of solidification of Fe–10Si–0·5Al (at-%) alloys. The dendritic growth of δ-Fe was clearly observed using this technique. The development of X-ray imaging techniques enables the solidification of various conventional cast alloys such as Al, Ni and Fe alloys to be observed and will be increasingly used to investigate solidification phenomena.     

Mobile Robot Control Architecture for Reflexive Avoidance of Moving Obstacles

In this paper, a three-layer (deliberative, sequencing, reflexive) architecture is adopted and the structure of the reflexive layer is discussed. The objective of this architecture is to extract the basic actions that require hard-real-time execution from non-real-time-allowed behaviors by separating them into the reflexive and sequencing layers, respectively. The reflexive layer consists of resources, actions, an action coordinator and a motion controller. To guarantee the hard-real-time execution, a set of simple actions and an action coordinator are designed using the functions provided in the RTAI (Real-Time Application Interface for Linux) environment. Also, an obstacle avoidance algorithm based upon data from a laser range scanner is developed. For the purpose of avoiding a moving obstacle, which is treated as a moving circle through segmentation and circularization processes, a Kalman filter is developed to estimate the distance and the heading of the center of the moving circle. The effectiveness and real-time characteristics of the proposed reflexive layer and the developed algorithms are examined through experiments using scattered stand-still obstacles as well as a moving human.     

Synthesis on forward kinematics problem algebraic modeling for the planar parallel manipulator: displacement-based equation systems

Based on a proven exact method which solves the forward kinematics problem (FKP) this article investigates the FKP formulation specifically applied to planar parallel manipulators. It focuses on the displacement-based equation systems. The majority of planar tripods can modeled by the 3-RPR parallel manipulator, which is a tripod constituted by a fixed base and a triangular mobile platform attached to three kinematics chains with linear (prismatic) actuators located between two revolute joints. In order to implement the algebraic method, the parallel manipulator kinematics are formulated as polynomial equation systems where the number of equations is equal to or exceeds the number of unknowns. Three geometrical formulations are derived to model the difficult FKP. The selected proven algebraic method uses Gröbner bases from which it constructs an equivalent univariate system. Then, the real roots are isolated using this last system. Each real solution exactly corresponds to one manipulator assembly mode, which is also called a manipulator posture. The FKP resolution of the planar 3-RPR parallel manipulator outputs six complex solutions which become a proven real solution number upper bound. In several typical examples, the resolution performances (computation times and memory usage) are given. It is then possible to compare the models and to reject one. Moreover, a number of real solutions are obtained and the corresponding postures drawn. The algebraic method is exact and produces certified results.     

Dinitrophenyl Triazoles – “A Class of Energetic Azoles”: Synthesis,Characterisation, and Performance Evaluation Studies

Energetic azoles have shown great potential as powerful energetic molecules, which find various applications in both military and civilian fields. This work describes the synthesis, characterization and performance evaluation of two energetic triazole derivatives, viz. N‐(2,4‐dinitrophenyl)‐3‐nitro‐1H‐1,2,4‐triazole ( 1a ) and N‐(2,4‐dinitrophenyl)‐3‐azido‐1H‐1,2,4‐triazole ( 1b ). The compounds were synthesized from 3‐nitro‐1,2,4‐triazole and 3‐azido‐1,2,4‐triazole, by a simple synthetic route and structurally characterized using FT‐IR and NMR (¹H, ¹³C) spectroscopy as well as elemental analysis. Thermal analyses on the molecules were performed using simultaneous TG‐DTA. Both compounds ( 1a , 1b ) showed good thermal stability with exothermic decomposition peaks at 348 °C and 217 °C, respectively, on DTA. The energetic and sensitivity properties of both compounds like friction sensitivities and heats of formation are reported. The heats of combustion at constant volume were determined using oxygen bomb calorimetry and the results were used to calculate the standard molar heats of formation (Δ_fH^m). The azido derivative ( 1b ) showed a higher positive heat of formation. The thermo‐chemical properties of the compounds as well as the thermal decomposition products were predicted using the REAL thermodynamic code.