E14 Lab 3
Prof. Paul Mitiguy
Spring 2007-2008
Page 1/4
Model:
The following figure shows a pair of pliers that consists of an upper rigid handle HU,
a lower rigid handle HL, an upper rigid jaw JU, and a lower rigid jaw JL.
Note: Since the applied load and the pair of pliers are both symmetric, the forces on the lower jaw are symmetric to the forces
on the upper jaw.
Frictionless revolute joints connect:
• HU and HL at point C
• HU and JL at point E
• HL and JU at point B
Frictionless slider joints connect:
• HU and JU at point A
• HL and JL at point D
The weight of the pliers is negligible
as compared to the magnitude of the
forces applied by human hands and
the forces applied to the sensor.
We model the pliers as gripping an object without pulling in the Nx direction. As a result,
the hands forces and the jaw forces are in the Ny direction only.
E14 Lab 3
Prof. Paul Mitiguy
Spring 2007-2008
Page 2/4
Identifiers:
To facilitate this analysis, right-handed orthogonal unit vectors Nx, Ny, Nz are fixed
in both JU and JL with Nx directed from A to B (or equivalently D to E), Ny directed from
D to A (or equivalently from E to B), and Nz parallel to all the pliers’ revolute joint axes.
Description
Nx measure of the position vector from S to D (or from R to A)
Nx measure of the position vector from D to C (or from A to C)
Nx measure of the position vector from C to B (or from C to E)
Nx measure of the position vector from B to Q (or from E to Q)
Nx measure of the Hand Force applied at R
-Ny measure of the Hand Force applied at R
Nx measure of the Hand Force applied at S
Ny measure of the Hand Force applied at S
Ny measure of the force from the sensor on the upper Jaw
Ny measure of the force from the sensor on the lower Jaw
Nx measure of the Reaction Force at B
Ny measure of the Reaction Force at B
Nx measure of the Reaction Force at C
Ny measure of the Reaction Force at C
Nx measure of the Reaction Force at E
Ny measure of the Reaction Force at E
Ny measure of the Reaction Force at A
Ny measure of the Reaction Force at D
Symbol
a
b
c
d
Rx
Ry
Sx
Sy
JUy
JLy
Bx
By
Cx
Cy
Ex
Ey
Ay
Dy
Type
Constant
Constant
Constant
Constant
Variable
Variable
Variable
Variable
Specified
Specified
Variable
Variable
Variable
Variable
Variable
Variable
Variable
Variable
Physics:
To analyze the pliers, we will use four free-body diagrams (four systems).
Value
70 mm
25 mm
25 mm
20 mm
s
E14 Lab 3
Prof. Paul Mitiguy
Spring 2007-2008
Page 3/4
Draw the external contact and distance forces for the following four diagrams.
Simplify and Solve:
Calculate the pliers’ mechanical advantage |JUy| / |Ry| = (a+b)*(b+c)/(b*d-c*(b+c+d))
Note: Please pass-in your calculations (feel free to use Autolev, Matlab, or other programs).
Result:
Mechanical Advantage
=
Output Force applied by the plier ' s jaws to the force sensor
Input Force applied by human hands to the plier ' s handles
=
( a + b )( b + c )
bd − c ( b + c + d )
E14 Lab 3
Prof. Paul Mitiguy
Spring 2007-2008
Page 4/4
Interpret and Design:
Using Matlab, Alplot (installed with Autolev), Excel, or a similar graphing
package,1 create four graphs, one for each of Ry vs. a, b, c, d, respectively. For the first
graph,use the measured values for b, c, d. For the second graph, use the measured values
for a, c, d. Similarly, create the third and fourth graphs. Vary the independent variable
from 15 to 25 mm.
When a = 70 mm and d = 20 mm, the
mechanical advantage is a function of b
and c as shown to the right. Find the
values of b and c that maximize the
pliers’ mechanical advantage and
determine its maximum.
Result:
b = ____ mm
c = ____ mm
Max Mechanical Advantage = ____
1
Links to tutorials for the graphing and software programs are on the class website.