Dynamics of a Stewart platform

The kinematics and dynamics of a Stewart platform supported by six pneumocylinders are considered. The differential equations of motion are written, and the forces providing the fulfillment of the formulated law of motion are calculated. The inertia and weight of pneumocylinders are introduced into consideration to refine the equations of motion. The obtained equations are used to study the motion of a loaded Stewart platform, providing the stability of this motion by means of feedback control. Some numerical examples are given.     

Continuous workspace analysis for parallel cable-driven Stewart-Gough platforms

Parallel cable-driven Stewart-Gough platforms consist of a end-effector which is connected to the machine frame by motor driven cables. Since cables can transmit only tension forces, at least m = n + 1 cables are needed to tense a system having n degrees-of-freedom. This results in a kinematical redundancy and leads to a (m – n)-dimensional solution space for the cable force distribution. For this reason, performing a workspace analysis requires advanced methods and is time consuming. However, reliable and robust algorithms are demanded to calculate the workspace for a given parameter set (winch positions and platform anchor points). Discrete methods are widely used to analyze the workspace. Singularities as well as cable collisions inside the workspace of a cable-driven Stewart-Gough platform are possible [1]. Therefore discrete methods may deliver wrong results due to the fact that intermediate points on the discrete calculation grids are neglected. In this paper, another approach is presented. The use of intervals avoids the problems described above and leads to reliable results. In the following the basic ideas of this continuous workspace analysis are shown. For practical application, e.g. in robotics, even more important is the parameter synthesis, i.d. the process of designing a robot for a predefined workspace. However, the workspace geometries are very complex and not intuitive in general. Here, the analysis methods are also extended for synthesis. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Force control of a fluidic muscle driven parallel platform

In this paper a new method for the force control of a parallel platform consisting of six fluidic-muscles of type RRPS is presented. Fluidic muscles require that the gas model as well as the rubber nonlinearities are included in the control scheme. Moreover, the control law for the gas flow in the proportional directional control valve in 3/3-way function needs to be taken into account. The present paper describes the basic dynamic models as well as testbed results for the existing fluidic-muscle parallel platform “HexaSpine” [3]. Here each leg is equipped with a force sensor, a pressure sensor and a magnetostrictive position encoder. The control scheme for the platform comprises six control loops for the six operated actuators with a model based force control each. It is shown that the aforementioned control scheme leads to a stable force control of the platform driven by fluidic muscles. As an application, the device will be employed in fields of biomechanics, as well as in general environments requiring physical simulation. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Direct Kinematic Solution of the Planar Stewart Platform with Coplanar Ground Points

1.IntroductionTheproblemforcomputingthepositionofaStewartPlatfromhasbeenwidelystudiedforvariouscases.InthispaPerwewinconsiderthecaseforwhichthegroundpoilltsarecoplanaxandtheffeationsofthelegsontheplatfromarecoplanar.Itissimplerthanthecoplanarplatformin[1]wherethegroundisnotneces88Iyaplane.DuetothissimplicitythecomputationcanbecarriedoutdirectlyavoidingthecomPotationofGroebnerbasisbystandardalgorithmandthenfromittodeduceconditinnfor4Ocomplexsolutionsispresented.Insection2wegivethepolynomiaJ…     

Workspaces of the Stewart platform in the 6D space of generalized coordinates

The kinematics and dynamics of the classical Stewart platform is studied. The platform is a rigid body supported by six rods of variable length. Well-known differential equations describing the motion of the platform are presented. The main attention is paid to an analysis of workspaces in the 6D space of generalized coordinates. The projections of these workspaces on spaces of lower dimension are found.     

Joint And Muscle Forces During Clenching

The masticatory system is highly redundant. Therefore, complete knowledge about the activation patterns of the chewing muscles belonging to a specific resultant bite force can only be gained either by simultaneous force- and EMG-measurement or with the help of optimization strategies. In this study, such EMG and force measurements were carried out with 10 test persons and the results compared to those computed with several objective functions. The results show an increase of the joint forces with an increase of the horizontal component of the resultant bite force. The test persons seem to favor energy minimization as control mechanism. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dynamic modeling of a Stewart platform using the generalized momentum approach

Dynamic modeling of parallel manipulators presents an inherent complexity, mainly due to system closed-loop structure and kinematic constraints.In this paper, an approach based on the manipulator generalized momentum is explored and applied to the dynamic modeling of a Stewart platform. The generalized momentum is used to compute the kinetic component of the generalized force acting on each manipulator rigid body. Analytic expressions for the rigid bodies inertia and Coriolis and centripetal terms matrices are obtained, which can be added, as they are expressed in the same frame. Gravitational part of the generalized force is obtained using the manipulator potential energy. The computational load of the dynamic model is evaluated, measured by the number of arithmetic operations involved in the computation of the inertia and Coriolis and centripetal terms matrices. It is shown the model obtained using the proposed approach presents a low computational load. This could be an important advantage if fast simulation or model-based real-time control are envisaged.     

Modelling and Flatness‐Based Control of a Carriage Actuated by Pneumatic Muscles

Pneumatic muscles are innovative tension actuators consisting of textile‐fibre reinforced vulcanised rubber tubing and connection flanges at both ends. They offer several advantages as compared to pneumatic cylinders: significantly less weight, no moving parts within the muscle, and higher maximum force. The main drawback is given by their non‐linear characteristics demanding for sophisticated non‐linear feedback control schemes. This contribution presents a non‐linear control concept for a carriage driven by two pneumatic muscles in parallel connection. First, the modelling of the muscle driven carriage is described in detail. For the resulting non‐linear model the differential flatness property is proven and utilised for a decoupled position and pressure trajectory control. Experimental results from an implementation of this flatness‐based control scheme at a test rig demonstrate the high tracking performance and point out the potential of this new actuator. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Classification of direct kinematics to planar generalized Stewart platforms

This paper presents the classification of direct kinematics for the planar generalized Stewart platform (GSP) which consists of two rigid bodies connected by three constraints between three pairs of points or lines in the base and the moving platforms. For each of the sixteen forms of planar GSPs, we give the explicit conditions on the parameters for the GSPs to have a given number of real solutions.     

Modeling,simulation and control a hydraulic servo system

Hydraulic actuators are widely used in industrial applications due to several advantages like large force and torque, high power to weight ratio, rapid and accurate response. In this paper a nonlinear model of a hydraulic servo system is developed by means of the associated differential equations and then simulated using Matlab techniques. The model describes the behavior of a servo system FESTO TP511 with MOOG-DDV633 servovalve and includes the nonlinearities of friction forces, valve dynamics, oil compressibility and load influence. The nonlinear model is used to design an optimal controller based on estimated state parameters through simulation. A digital control platform based on Atmel ATmega8535 microcontroller is used to compare the behavior of hydraulic system under PD and optimal control. The control platform was designed like an interface between PC and process: the control algorithm runs on PC and the digital platform assures amplifying, filtering and data communication functions. Both simulation and experimental results are provided to show the effectiveness of the proposed model and control method. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Characterization of disk brake noise behavior via measurement of friction forces

Squealing of disk brakes is a major problem in the field of vehicle design. It is commonly acknowledged, that this squeal is initiated by instability due to friction forces between the pads and the disk, leading to self excited vibrations. This work addresses the mechanical work of these friction forces in order to draw conclusions for the investigation of the noise behavior of disk brakes. Therefore a multi degree of freedom model is used to compare its stability behavior with the frictional work at the pads. The results obtained are applied to experiments in which, on the one hand brake pads with integrated piezoceramic actuators cause a broad band excitation and, on the other hand, dynamic pad velocities/accelerations and friction forces are measured. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mathematical Modeling and Simulation of a Flexible Shaft-Flexible Link System With End Mass

In this study, the equation of motion of a single link flexible robotic arm with end mass, which is driven by a flexible shaft, is obtained by using Hamilton's principle. The physical system is considered as a continuous system. As a first step, the kinetic energy and the potential energy terms and the term for work done by the nonconservative forces are established. Applying Hamilton's principle the variations are calculated and the time integral is constructed. After a series of mathematical manipulations the coupled equations of motion of the physical system and the related boundary conditions are obtained. Numerical solutions of equations of motion are obtained and discussed for verification of the model used.     

A comparison of static optimization criteria for resolving the 3D muscle redundancy problem during human gait

In this paper, different approaches of static optimization for predicting muscle forces during human walking are investigated. In order to better reflect the true mechanics of the human body, a three-dimensional musculoskeletal model of a single leg is developed. The joint moments generated by muscles during walking are computed from inverse dynamics. The muscle force is estimated by different optimization criteria, each satisfying the moment constraints at all joints and the lower and upper muscle force constraints. Several polynomial and non-polynomial criteria frequently used in literature are studied. Then the results obtained from these calculations are compared with each other. This paper provides an overview of the effects of different optimization criteria on the 3D muscle force distribution problem during human walking. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On iterative refinements for spectral sets and spectral subspaces

Stewart (1971) and Demmel (1987) have proposed iterative procedures for refining invariant subspaces of Hilbert space operators and matrices respectively. In this paper, modifications are proposed for these procedures which facilitates their application to bounded Banach space operators. Under regularity conditions (which could include densely defined closed operators) it is shown that the modifications perform as well as or better than the procedures of Stewart and Demmel.     

Fuzzy-Based Analysis of a Hill-Type Muscle Model

Among the most challenging problems in present day mechanics is the realistic simulation of the human kinetic behavior which requires correct modeling of the muscles – the human actuators. We are, therefore, implementing and validating a 1-D massless Hill-type muscle model in the program Neweul-M². As a part of this effort, various anatomical and physiological parameters need to be chosen prior to the simulation. These parameters are always subject to natural variability or scatter. Therefore, it is important to consider those parameters as uncertain fuzzy parameters and then determine the sensitivity measures of the parameters involved in various simulation scenarios using the program Famous. The applied sensitivity analysis quantifies the influence of individual parameters or subsets of parameters on the output quantity of interest. Thus, this analysis identifies those parameters with large influence on the simulation response of muscles which, therefore, needs to be chosen very carefully. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On parallel Branch and Bound frameworks for Global Optimization

Branch and Bound (B&B) algorithms are known to exhibit an irregularity of the search tree. Therefore, developing a parallel approach for this kind of algorithms is a challenge. The efficiency of a B&B algorithm depends on the chosen Branching, Bounding, Selection, Rejection, and Termination rules. The question we investigate is how the chosen platform consisting of programming language, used libraries, or skeletons influences programming effort and algorithm performance. Selection rule and data management structures are usually hidden to programmers for frameworks with a high level of abstraction, as well as the load balancing strategy, when the algorithm is run in parallel. We investigate the question by implementing a multidimensional Global Optimization B&B algorithm with the help of three frameworks with a different level of abstraction (from more to less): Bobpp, Threading Building Blocks (TBB), and a customized Pthread implementation. The following has been found. The Bobpp implementation is easy to code, but exhibits the poorest scalability. On the contrast, the TBB and Pthread implementations scale almost linearly on the used platform. The TBB approach shows a slightly better productivity.     

Numerical simulation of the sedimentation of a tripole-like body in an incompressible viscous fluid

In this note, we discuss the application of a methodology combining distributed Lagrange multiplier based fictitious domain techniques, finite-element approximations and operator splitting, to the numerical simulation of the motion of a tripole-like rigid body falling in a Newtonian incompressible viscous fluid. The motion of the body is driven by the hydrodynamical forces and gravity. The numerical simulation shows that the distribution of mass of this rigid body and added moment of inertia compared to a simple cylinder (circular or elliptic) plays a significant role on the particle-fluid interaction. Apparently, for the parameters examined, the action of the moving rigid body on the fluid is stronger than the hydrodynamic forces acting on the rigid body.     

Hidden semi-Markov model-based methodology for multi-sensor equipment health diagnosis and prognosis

This paper presents an integrated platform for multi-sensor equipment diagnosis and prognosis. This integrated framework is based on hidden semi-Markov model (HSMM). Unlike a state in a standard hidden Markov model (HMM), a state in an HSMM generates a segment of observations, as opposed to a single observation in the HMM. Therefore, HSMM structure has a temporal component compared to HMM. In this framework, states of HSMMs are used to represent the health status of a component. The duration of a health state is modeled by an explicit Gaussian probability function. The model parameters (i.e., initial state distribution, state transition probability matrix, observation probability matrix, and health-state duration probability distribution) are estimated through a modified forward–backward training algorithm. The re-estimation formulae for model parameters are derived. The trained HSMMs can be used to diagnose the health status of a component. Through parameter estimation of the health-state duration probability distribution and the proposed backward recursive equations, one can predict the useful remaining life of the component. To determine the “value” of each sensor information, discriminant function analysis is employed to adjust the weight or importance assigned to a sensor. Therefore, sensor fusion becomes possible in this HSMM based framework.