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On The Use Of Natural Coordinates In The Optimum Synthesis Of Mechanisms
No full textThis paper deals with the use of natural coordinates for the synthesis of mechanisms using optimization methods. It will be shown that an approach based on this kind of coordinates has many interesting aspects. The modeling of a mechanism with natural coordinates, like any other multi-body system, is carried out by means of a system of algebraic constraint equations. These are complemented by additional equations describing the requirements of the mechanism. All types of requirements - paths, function generation, body guidance, correlation between members - may be given in this way, so that there is a unified method for treating any kind of synthesis. An interesting method is developed here for kinematic analysis of candidate mechanisms. According to this method, kinematic analysis is carried out in the sense that only constraint equations are satisfied exactly, while requirements are satisfied at best. This corresponds to finding the motion of the candidate mechanism that is `closest' to established requirements. This method is then reduced to the solution of the Initial Value Problem (IVP) of a proper system of Ordinary Differential Equations (ODEs). Lastly, the design space (i.e., the space of the design parameters) also takes advantage of the natural coordinates approach. It is based on the initial values of the natural coordinates themselves rather than on link lengths. This avoids the need to assemble the mechanism in the initial position (and associated branching problems), gives more uniform spanning of the solution space, and guarantees that at least the starting configuration for the ODEs IVP exists and is known. Three examples are given: a four-bar linkage generating a straight path, the same type of linkage generating a square angle (both without correlation), and a six-link Stephenson's mechanism producing a function with a dwell range
A SYMBOLIC APPROACH FOR AUTOMATIC GENERATION OF THE EQUATIONS OF MOTION OF MULTIBODY SYSTEMS
No full textThis paper describes a collection of methods and procedures for the automatic generation of the equations of motion of multibody systems using general-purpose Computer Algebra Software. A brief review of existing symbolic multibody systems is given, and advantages and disadvantages of symbolic approaches compared with numerical ones are discussed. Then, a set of methods for symbolic modeling of multibody systems is explained. The first step of the modeling procedure consists of the description of the multibody system, by defining objects (such as points, vectors, rigid bodies, forces and torques, special objects) and the relationships between them (kinematic chains, constraints). The second step is the derivation of the equations of motion, which can be performed in a quasiautomatic way. A further step is the linearization of the equations and the calculation of the system's frequency response functions. By way of example, a dynamic model of the motorcycle is developed, obtaining the nonlinear equations of motion in a dependent coordinates' formulation. Next, the equations of motion are linearized and reduced to an independent formulation, reobtaining the well known Sharp's model of the straight running of the motorcycle. Root loci and frequency response functions are also calculated. This example demonstrates the power of the given symbolic procedures and shows how a model suitable for stability, handling and control analysis can be developed quickly and easily. The procedure described in this paper has been implemented in a Maple package called 'MBSymba', which is available on the web page www.dim.unipd.it/lot/mbsymba.html
Spacecraft High Precision Optimized Control Design for Free-falling Test Mass Tracking in Lisa-Pathfinder Mission
No full textLISA (Laser Interferometer Space Antenna) will be the first space mission for the in-flight detection of gravitational waves. In order to reduce the mission risk, some of the key technologies needed for LISA will be tested by means of the LISA Test-flight Package (LTP) on board the LISA Pathfinder mission (SMART- 2). The goal of the LISA Pathfinder is to provide in- flight testing of the free-fall level of a reference Test Mass (TM) to within a factor 10 from the LISA top- science requirement.
One of the critical technologies to be tested is the Test Masses Drag-Free and Attitude Control System (DFACS), which is the system that has to provide the test masses inertial insulation through satellite relative position control up to the nanometer level.
The system analyzed in the paper is modelled as a multibody made of the satellite, actuated through thrusters, and two test masses, kept at a fixed relative distance by using a capacitive actuation. The paper presents a new control design procedure for this MIMO system. The procedure, based on a multi- objective optimization, yields to controllers that achieve the prescribed levels of performance in terms of disturbance rejection, robustness and phase margin
Experimental and Theoretical Study of Motorcycle Transfer Functions for Handling Evaluation
No full textA General Method for the Evaluation of Vehicle Manoeuvrability with Special Emphasis on Motorcycles
No full textThis paper presents a novel approach to the assessment of the manoeuvrability of vehicles which is not based on the simulation of open-loop manoeuvres, nor does it rely on the modelling of the driver as a control system. Instead, the essence of the method is the solution of a two-point optimal control boundary value problem, in which a vehicle, subject to physical constraints like tyre adherence and road borders, among others, is required to go between given initial and final positions as fast as possible. The control inputs - i.e., the driver's actions - that make the vehicle move between the two states in the most efficient way are found as a part of the solution procedure and represent the actions of a sort of ideal, perfect driver. The resulting motion is called the optimal manoeuvre and, besides being the most efficient way that the given vehicle has for travelling between the two points according to the chosen optimal criterion, may be taken as a reference for meaningful comparisons with other vehicles. The value of the penalty function, used to define the optimal condition occurring at the optimal manoeuvre, may be taken as a measure of manoeuvrability or handling. With this approach the manoeuvrability properties are established as intrinsic to the vehicle, being defined with respect to an ideal perfect driver. Some possible forms of the penalty function, which means slightly different concepts of manoeuvrability and handling, are discussed. In the end, the case of motorcycles and some examples of optimal manoeuvres are given
Evaluation of Motorcycle Manoeuvrability with the Optimal Manoeuvre Method
No full textGLOBAL MOBILITY DATABAS
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