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Session 1566

Adjustment Calculus - an Interesting Part of Kinematics

Wieslaw M. Szydlowski

University of Nebraska-Lincoln Mechanical Engineering Department

Abstract

Little known method is explained for finding velocity and acceleration from positions of a point which are equidistant in time. The adjustment calculus can be a powerful tool to reduce the effect of measurements errors on the estimations of the velocity and the acceleration. In-class exercises in kinematics may brings fun to all participants.

1 Introduction

The general purpose of a mechanism is to move a machine element from one position to another. The type of motion that the element undergoes may be given, or it may be left for the designer to choose. In either case, it is often desirable to know how the velocity and acceleration of the element vary. There is a large variety of graphical and analytical methods which can be used to solve this type of problems. However, the methods become unsuitable if the velocity and the acceleration of a point needs to be determined from a sequence of displacements measured at equal intervals of time.

The examples that follow are taken from various areas, and all represent the problems in which velocity and acceleration have to be determined from the displacements equidistant in time.

(A) A robotic vision system is tracking a fast moving object. The coordinates of a chosen point(s) on this object can be determined by a computer from the frames recorded by a vison system every 30 th of a second. To predict the position of the object, the velocities and accelerations of the recent point(s) on the trajectory have to be accurately estimated. The problem may be considerably complicated when the coordinates of the points of interest are measured with significant errors caused by, for example, poor resolution and image blurring.

(B) A study of human or animal motion has to be conducted, when the coordinates of the points marked on extremities are determined from the consecutive frames of a videotape. Using information about positions of the extremity obtained for equal time increments, the researchers may develop acceleration diagrams for the examined individual, which can be used for diagnostic purposes.

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Szydlowski, W. M. (2000, June), The Adjustment Calculus – An Interesting Part Of Kinematics. Paper presented at 2000 Annual Conference, St. Louis, Missouri. 10.18260/1-2--8160