Go to   Fun_Math Content Table   Trisecting an Angle   Mechanical Linkages

2 links were credited to Laisant,and the third one is the improvement of the Link #2 using the idea of Kempe's link.

One of the Laisant's Link is shown in the figure shown below.

APB is placed on the angle to be trisected.

There are grooves along CQ and DV.
(shown in red lines)
Joints at T and R are free to slide
along these grooves.
Rods ED and FC are straight and continuous.

Due to symmetry, angle EPF is one third of angle APB.

You can see the process in animation.

******** Laisant_1_trisection_desc.dwg ********

To create this drawing and animation:
Then from command line, type Laisant_1
For a quick look to see how the mechanism works, type test_Laisant_1

Animation file creation:animation_Laisant_1

#### Note on Program execution:    Laisant_1

During the execution of Laisant_1,   3 viewports as shown appear.
at left:             Global viewport:   This shows the global picture.
at upper right:   Test point view:   showing the target line.
at lower right:   Cursor move point:   Cursor will move the point of the link

****** Laisant_1_viewport.dwg ******

#### Example: 105 degrees case

Input @2<105. --> for 105 degrees case

****** Laisant_1_trisection_105_deg.dwg ******

One of the Laisant's Link is shown in the figure shown below.

You can see the process in animation.

****** Laisant_2_trisection_desc.dwg ******

To create this drawing and animation:
Then from command line, type Laisant_2
For a quick look to see how the mechanism works, type test_Laisant_2

Animation file creation:animation_Laisant_2

#### Example Run: 105 degrees case:

---->input @2<105.. -->105 degrees case

****** Laisant_2_trisection_105_deg.dwg ******

One of the Laisant's Link is shown in the figure shown below.

Using Kempe's two crossed parallelogram
,it is possible to eliminate groove on PD, and replace two rods UT & UR by 3 rods as shown.
Now we have linkage without sliding groove,which is a nuisance.

You can see the process in animation.

****** Laisant_desc.dwg ******

To create this drawing and animation:
Then from command line, type Laisant
For a quick look to see how the mechanism works, type test_Laisant

Animation file creation:animation_Laisant

#### Example Run: 120 degrees case:

---->input @2<120.. -->120 degrees case

****** Laisant_trisection_120_deg.dwg ******

#### References

1. Yates, Robert Carl : "The Trisection problem", p 38-39. p 41-42

Go to   Fun_Math Content Table   Trisecting an Angle   Mechanical Linkages

All questions/suggestions should be sent to Takaya Iwamoto

Last Updated Nov 22, 2006