David G. Beale

Synthesis and analysis of the five-link rear suspension system used in automobiles

Abstract The paper deals with the optimum kinematic synthesis and analysis of the five-link independent suspension system (also known as “multilink” suspension, mechanism commonly symbolized 5S–5S). The synthesis goal is fulfilling a minimum variation of the wheel track, toe angle and camber angle during jounce and rebound of the wheel. Two solutions obtained by synthesis are analyzed and compared to an existing solution, and the displacement, velocity and acceleration of the wheel carrier relative to the car body are determined, together with the variation of the momentary screw axis and the rear axle roll-center height. Both the kinematic synthesis and the analysis are performed in a simplified, easy to program manner, using a fictitious mechanism that has all the links dismounted from their joints.

Optimum synthesis of the four-bar function generator in its symmetric embodiment: the Ackermann steering linkage

The problem of optimum synthesis of the planar four-bar function generator is investigated and the practical case of the Ackermann steering linkage considered as an example. The reduced number of design parameters of this symmetric four-bar linkage allowed inspecting the design space of various types of objective functions through 3D representations, and their properties suggestively highlighted. For practical purposes, the numerical results were summarized in a set of parametric design-charts useful to the automotive engineer in conceiving the steering linkage of a new vehicle.

Structural Analysis of a Two-dimensional Braided Fabric

Two-dimensional-braid geometry is analyzed. The cover factor of a fabric braided on a particular braider depends on three variables: braid angle, helical length, and braid diameter; however, only two of the three are independent because of an equation of constraint. The cover factor of an existing braid is a function of braid angle and diameter and maintains a constant helical length between its tensile and compressive jammed states. A stable jammed state with maximum crimp is found to exist when the braid angle is 45° and the helical length is a minimum. When the braid diameter is held constant by braiding on a constant-diameter mandrel, the cover factor is increased by decreasing the helical length or increasing the braid angle. The cover factor is directly related to the fabric width as a single independent variable. When the yarn cannot be considered as a flat strip but must instead be considered to have a circular cross-section, the maximum cover factor in the jammed state is shown to be 0.82.

BASE DYNAMIC PARAMETER ESTIMATION OF A MACPHERSON SUSPENSION MECHANISM

Summary A MacPherson suspension mechanism is modeled as a two degrees of freedom spatial mechanism. Its dynamic response under two excitement forces is simulated with the motion equations in Euler Parameters with the off-the-center-of-mass body-fixed coordinates derived in this paper. Simulation results are sampled and input into a numerical estimation routine based on singular value decomposition (SVD). Accurate numerical estimation results are achieved. A set of base dynamic parameters in symbolic expressions is also derived from the numerical results utilizing the concepts of mass transfer and moments of inertia transfer. This makes it possible to apply the estimation results to any MacPherson suspension mechanism with the same joint configuration. The potential applications of the symbolic base dynamic parameters in suspension design are also considered.

Teeth-Number Synthesis of a Multispeed Planetary Transmission Using an Estimation of Distribution Algorithm

The gear-teeth number synthesis of an automatic planetary transmission used in automobiles is formulated as a constrained optimization problem that is solved with the aid of an Estimation of Distribution Algorithm. The design parameters are the teeth number of each gear, the number of multiple planets and gear module, while the objective function is defined as the departure between the imposed and the actual transmission ratios, constrained by teeth-undercut avoidance, limiting the maximum overall diameter of the transmission and ensuring proper spacing of multiple planets. For the actual case of a 3+1 speed Ravigneaux planetary transmission, the design space of the problem is explored using a newly introduced hyperfunction visualization technique, and the effect of various constraints highlighted. Global optimum results are also presented.

A General Method for Estimating Dynamic Parameters of Spatial Mechanisms

Dynamic equations of motion require a large number of parameters for each element of the system. These can include for each part their mass, location of center of mass, moment of inertia, spring stiffnesses and damping coefficients. This paper presents a technique for estimating these parameters in spatial mechanisms using any joint type, based on measurements of displacements, velocities and accelerations and of external forces and torques, for the purpose of building accurate multibody models of mechanical systems. A form of the equations of spatial motion is derived, which is linear in the dynamic parameters and based on multibody simulation code methodologies. Singular value decomposition is used to find the ‘essential parameter set’, and ‘minimum parameter set’. It is shown that a simulation of a four-bar mechanism (with spherical, universal, and revolute joints) and based on the estimated parameters gives accurate response.

Constrained optimization problem solving using estimation of distribution algorithms

Two variants of estimation of distribution algorithm (EDA) are tested solving several continuous optimization problems with constraints. Numerical experiments are conducted and comparison is made between constraint handling using several types of penalty and repair operators in case of both elitist and nonelitist implementation of the EDAs. Graphical display and animations of representative runs of the best and worst performers proved useful in enhancing the understanding of how such algorithms work.

A new method to determine the base inertial parameters of planar mechanisms

Abstract This paper presents a simple method to determine the closed form base inertial parameters of general planar mechanisms. Based on mass transfer and moment of inertia transfer concepts, inertial parameter regrouping is physically interpreted. The relationships between inertial parameters of two jointed links are developed, leading to two propositions for inertia parameter regrouping of general moving links. For the unique configuration of moving links jointed to ground, two more propositions are presented. From these four propositions, base inertial parameters of a general planar mechanism can be easily formulated by inspection of the mechanism configuration. An equation to calculate the number of base parameters is also presented. Base parameters are estimated by this new method for several example planar mechanisms. This method gives all base parameters for general planar mechanisms, though in certain cases, it may overestimate the number of base parameters because certain kinematic configurations cause further regrouping of base parameters.

Experimental observations of a flexible slider crank mechanism at very high speeds

A slider crank mechanism has been constructed and operated for the purpose of investigating steady state rod bending vibration induced by a very high speed crank. Features include a combination flywheel and adjustable length crank, a thin aluminum connecting rod, and a piston sliding on steel rod slide axes. A strain gage on the rod and magnetic pickup on the crank sensed rod strain and crank speed, respectively.For this system configuration, experimental results are categorized as small, intermediate and large crank length response. Small and intermediate cranks response was amplified due to a large superharmonic component of twice the crank speed frequency and at crank speeds near 1/2 the first natural frequency of the rod. Beyond that speed, period doubling occurred over a range of speeds for intermediate length cranks. The occurrence of period doubling was experimentally sudden and audibly noticeable, and characterized by the onset of frequency components of 1/2, 3/2, 5/2, and 7/2 times the crank speed. For large crank sizes of 0.5, 1, and 2 inches an amplified response also appeared in each at a certain speed, but at speeds lower than in the small and intermediate crank cases. Larger cranks required more frequency components to describe the response than smaller cranks. Experimental responses were correlated with computer simulations of a one mode nonlinear ordinary differential equation model, and over a wide range of speeds and for a representative of a small, intermediate, and large crank length.

Visualization of hypersurfaces and multivariable (objective) functions by partial global optimization

Hypersurfaces of the type z=F(x1,...,xn), where F are single-valued functions of n real variables, cannot be visualized directly due to our inability to perceive dimensions higher than three. However, by projecting them down to two or three dimensions many of their properties can be revealed. In this paper a method to generate such projections is proposed, requiring successive global minimizations and maximizations of the function with respect to n-1 or n-2 variables. A number of examples are given to show the usefulness of the method, particularly for optimization problems where there is a direct interest in the minimum or maximum domains of objective functions.