## Masters Theses

## Abstract

"The purpose of this thesis is to find a method of synthesis, for a four-bar mechanism, so that the mechanism that is synthesized will have a low value of jerk. In the field of synthesis there has been little or no effort made to consider jerk when designing mechanisms.

Jerk is defined as the time rate of change of acceleration. Jerk can also be expressed as being proportional to the time rate of change of the inertia forces. When the jerk is large the effect on the link of a mechanism is the same as that of an impact load. Another effect of jerk is the excessive wear at the pin connections.

The model used to study jerk is the four-bar mechanism and in particular the crank-lever mechanism. A crank-lever mechanism has one fixed link (the ground link), one link that rotates (the crank), one link that oscillates with plane motion (the coupler), and one link that oscillates with rotary motion (the lever). As the crank rotates the lever oscillates through an angle θ. The advance swing of the lever take place during a larger angle of crank rotation than the return swing of the lever, so we have a quick-return mechanism. The time ratio determines an angle α which along with θ specifies a family of mechanisms. A family of mechanisms is a group of mechanisms having the same angles θ and α, but having different proportions. It is assumed that some criterion can be found that will predict or determine which mechanism in a family will have the lowest value of maximum jerk. For the analysis four different families were chosen, each fami1y contains ten mechanisms.

The velocities, accelerations, and jerks for a four-bar mechanism can most readily be determined by graphical means. However, the graphical methods become quite tedious when they must be repeated many times. For this reason, analytical equations were derived that could be used on the digital computer. These equations were derived by writing position vector equations, for a four-bar; and differentiating once to obtain the angular velocity, differentiating twice to determine the angular acceleration, and differentiating a third time to determine the angular jerk. A program can be written for the IBM 1620 that will calculate the values of jerk for a mechanism. These calculated values were then plotted against the crank angle. From the trend of these curves the methods of synthesis were determined"-- Abstract pp. ii-iii

## Advisor(s)

Charles L. Edwards

## Committee Member(s)

Bill L. Atchley

Archie R. Graham

Ralph E. Schowalter

## Department(s)

Mechanical and Aerospace Engineering

## Degree Name

M.S. in Mechanical Engineering

## Publisher

Missouri School of Mines and Metallurgy

## Publication Date

1963

## Pagination

viii, 107 pages

## Note about bibliography

includes bibliographical references (page 88)

## Rights

© 1963 Ronald D. Brenner, All rights reserved.

## Document Type

Thesis - Open Access

## File Type

text

## Language

English

## Thesis Number

T 1477

## Print OCLC #

5950758

## Recommended Citation

Brenner, Ronald D., "Methods for synthesizing a four-bar mechanism so it will have a low value of jerk." (1963). *Masters Theses*. 5947.

https://scholarsmine.mst.edu/masters_theses/5947