Effect of variation of link lengths and stiffness on the gearing ratio of a four bar mechanism with application to aircraft trim tabs

Abstract

Kinematic chains or mechanisms have conventionally been analyzed comprising of links that behave as rigid members and links assumed to be built at nominal sizes. Such mechanisms, articulating entirely from rigid-body translations and/or rotations and nominally established links may not closely represent the actual real life manufactured parts with tolerances and joint clearances. It is important to identify the allowable variations in the linkages especially when the end-effector of the mechanism generates a path or a function and/or a tightly controlled gearing ratio or mechanical advantage is required. In this study, the band of solutions that can be obtained from the variation in lengths of linkages and the effect of stiffness is generated to better understand the quality of the mechanism performance. The application of four bar mechanism in an aileron trim tab system that utilizes a rotatory actuator to move the tab surface is used to demonstrate the band of solutions. Then CATIA VS is used to layout the geometry and design the linkages within the prescribed airfoil. The MSC Adams is used to calculate the initial gearing ratio and for validation of values. A Matlabgcode is developed and used to analyze the effects of the variation of lengths and stiffness of linkages on the tab speed using closed form algebraic solution. Finally, a comparison is made to illustrate and quantify the effects of link lengths and stiffness on the gearing ratio/mechanical advantage of the system.