Marc J. Richard

Analytic Form of the Six-Dimensional Singularity Locus of the General Gough-Stewart Platform

The determination of the 6D singularity locus of the general Gough-Stewart platform is discussed in this article. The derivation of the velocity equation and the corresponding Jacobian matrices is first presented. Then a new procedure is introduced to obtain the analytical expression of the singularity locus, which is a function of six variables (x,y,z.,Φ,θ,ψ), using the velocity equation. Examples are also given to illustrate the results obtained. Gough-Stewart platforms can be used in several robotic applications as well as in flight simulators. The determination of the singularity locus is a very important design and application issue.

Dynamic Analysis of a Manipulator in a Fluid Environment

The computation of the generalized forces produced by a fluid acting on the links of manipulators is considered here. The evaluation of these forces is necessary for the controller of an underwater manipulator (partially or totally immersed). This article presents an approximate method for the computation of buoyancy in local coordinates. The drag forces are computed by numerical integration of the local drag force. Numerical integration is necessary here to achieve a good precision. A new local reference frame is also added on each link to allow an easy description of the geometry of the links. When those computations are included in the dynamic model, a compromise must be made between computation time and precision, because this inclusion may result in doubling or tripling the number of operations to be performed in comparison with a standard dynamic algorithm.

Free vibrational analysis of axially loaded bending-torsion coupled beams: a dynamic finite element

Abstract In this article, a dynamic finite element formulation for the free vibration analysis of axially loaded bending-torsion coupled beams is presented. Based on the Euler–Bernoulli and St. Venant beam theories, the exact solutions of the differential equations governing the uncoupled vibrations of an axially loaded uniform beam are found. Then, employing these solutions as basis functions, the analytical expressions for uncoupled bending and torsional dynamic shape functions are derived. Exploiting the principle of virtual work, together with the variable approximations based on the resulting shape functions, leads to a single frequency dependent element matrix which has both mass and stiffness properties. The application of the theory is demonstrated by an illustrative example of a bending-torsion coupled beam with cantilever end conditions, for which the influence of axial force on the natural frequencies is studied. The correctness of the theory is confirmed by the published results and numerical checks.

An optimization method designed to improve 3-D vehicle comfort and road holding capability through the use of active and semi-active suspensions

The primary purpose of this paper is to analyze the effects of vibrations on the comfort and road holding capability of road vehicles as observed in the variation of different parameters such as suspension coefficients, road disturbances, and the seat position. This study required the development of a mathematical model to simulate the dynamic behavior of a 3-D vehicle. With this model, various types of non-linear suspensions such as active and semi-active suspensions may be investigated. The results obtained from the simulation of the 3-D vehicle demonstrate that the use of active and semi-active suspension models on road vehicles prove to be beneficial for comfort without unduly compromising road holding capability.

A general vector-network formulation for dynamic systems with kinematic constraints

Abstract The vector-network method is a simple, systematic procedure for formulating the equations of motion of dynamic mechanical systems. The method serves as a basis for “self-formulating” computer programs, useful in computer-aided design, which simulate system response, given only the system description as input. The method in this paper includes kinematic constraints and is a significant extension to earlier formulation techniques, which are seen to be special cases of this method. A computer program, RESTRI, has been developed for two- and three dimensional constrained systems; a flowchart and computer example are included. A similarity is observed between the vector-network equations of motion and those obtained by Chace for the DRAM program.

A Dynamic Finite Element (DFE) method for free vibrations of bending-torsion coupled beams

Abstract In this paper, a Dynamic Finite Element (DFE) formulation for the free vibration analysis of bending-torsion coupled beams is presented. First, the exact solutions of the differential equations governing the uncoupled vibrations of a uniform beam are found. The employment of these solutions as basis functions leads to the appropriate frequency dependent shape functions which can then be utilized to find the nodal approximations of variables. By exploiting the Principle of Virtual Work (PVW), the elementary Dynamic Stiffness Matrix (DSM) is then obtained which has both mass and stiffness properties. The implementation of the derived DFE matrices in a program is discussed with a particular reference to the Wittrick–Williams algorithm. The application of the theory is demonstrated by illustrative examples wherein a substantial amount of coupling between bending and torsion is highlighted. The correctness of the theory is confirmed, to a high degree of accuracy, by published results and numerical checks.

A survey of simulation programs for the analysis of mechanical systems

In this paper, several general-purpose computer programs for the generation of the response of dynamic systems are discussed. The basic theoretical principles of dynamics are evaluated from a topological point of view and the dynamical formalisms of the major general multibody programs are examined. Finally, a brief chronological survey of some general-purpose computer programs is presented.

The vector-network method for the modelling of mechanical systems

This paper presents an extension of the vector-network approach to the problem of motion prediction. The entire procedure is a basic application of concepts of graph theory in which laws of vector dynamics have been combined. A comprehensive mathematical model for the systematic formulation of the equations of motion of dynamic three-dimensional constrained multi-body systems is derived. The method embodies simultaneously the three-dimensional inertial equations associated with each rigid body and the kinematic constraints into a symmetrical format yielding the differential equations governing the response of the system. The modelling technique is thoroughly described in this work and its validity is impartially established.

A Bernoulli-Euler Stiffness Matrix Approach for Vibrational Analysis of Spinning Linearly Tapered Beams

This paper presents a Dynamic Finite Element (DFE) formulation, based on the Dynamic Stiffness Matrix (DSM) approach, for vibrational analysis of spinning beams. The constituent members are considered to be linearly tapered as well as centrifugally stiffened. A non-dimensional formulation is considered, and the frequency dependent trigonometric shape functions are used to find a single frequency dependent element matrix (called DSM) which has both mass and stiffness properties. An adapted bisection method based on a Sturm sequence root counting technique, is used to find the first four out-of-plane flexural natural frequencies of a cantilevered linearly tapered (in height) beam for different non-dimensional rotating speeds. The results have been compared to those found by finite elements method using Hermite beam elements. Much better convergency rates are found by this method when comparing to conventional finite element methods.© 1997 ASME

A multibody dynamics model to assess the impact of road unevenness on the efficiency of a semitrailer truck

An open source multibody model of a semi-trailer truck with 331 degrees of freedom was built and within it a dynamic tyre model has been implemented. The truck model was calibrated and validated by an on-road experimental campaign of coastdown tests. The signal from a photodetector and ten accelerometers, the weight distribution, meteorological data, and the longitudinal profile have been collected. The purpose of the model is to obtain the relationships between the longitudinal road profile and fuel consumption, vehicle wear, passenger health, and safety. A subsequent study demonstrated the capacity of the model to fulfil its purpose.