Linear Bearing Free Body Diagram (FBD) Problem

Reading: Free Body Diagrams Guidelines

Overview:

Linear slides can be subject to jamming (like screen doors). This is the reason many designers prefer rotary pivots whenever possible. However, if one would like to build a linear slide that does not jam, one needs to understand the reasons behind jamming.

In this assignment each student will analyze a Linear Slider, which is similar to the one shown in lecture. The overall objective of the assignment is to identify how to build good Linear Sliders that do not jam, and to develop skills in applying Free Body Diagrams (FBD). But do NOT forget, it is often better to replace a linear bearing with a rotary bearing when possible.

Analysis Problem:

Consider the linear slide shown in the sketch below in blue. The slider is held in place by two bearings shown in red, and a horizontal force, F, is exerted at a distance h from the bearings. Determine under what conditions the slider will move to the right.

Assumptions:

• • You can assume quasi-static analysis but you will need to consider the effect of friction. In quasi-static analysis one neglects acceleration forces. Thus the sum of moments and forces are equal to zero (actually they are just greater than zero in directions of impending motion).

  • Gravity can be neglected. Assume the slider is mounted horizontally as shown in lecture.

  • Assume Coulomb friction, where F_friction = mN

where m is a given coefficient of friction, and N is the normal force. For this analysis the static and dynamic coefficients of friction can be considered the same.

• • The thickness d is much less than h. Therefore for the purposes of analysis one can let d go to zero. (the overall results do not change much if d is larger, but it makes the equations harder to solve)

Steps In Analysis

The assignment will be graded on clarity, neatness, as well as the final result. Each solution should include:

• • A brief description of the problem, including a copy of the main figure below.

  • A Free Body Diagram (FBD) of the Slider. Show all forces applied onto the slider. Make sure to show all forces at the point where they are being applied and in the direction they are being applied onto the slider.

• Setup all equations for quasi-static planar analysis. These equations are: ΣF_x, ΣF_y, and ΣM are equal to zero or just greater than zero in the direction of motion.

• Solve the equations to find the conditions at which the slide will move.

• Based upon your results, discuss the important parameters one needs to consider when designing a linear slide. In particular, what parameters should be large, and which ones should be small?

Students are encouraged to pickup the Linear Slides in the Design Studio and feel the jamming effect themselves. Look carefully to see where the contact points which are indication of the load path in the mechanism.