Go to   Fun_Math Content Table   Trisecting an Angle   Mechanical Linkages

Kempe's Link is shown in the figure shown below.

In this simple link, the length of 4 rods are set such that
AB = CD and AC = BD.
Then, when D moves with point A as a pivot,
angle BAC is always equal to angle BDC.

You can see the process in animation

****** Kempe_4_rods_desc.dwg ******

To create this drawing and animation:
Then from command line, type 4_rods

Animation file creation:animation_4_rods

Kempe's Link is shown in the figure shown below.

Two more rods (AF & FE) are added such that
trapezoid ABCD and AFBE are similar.

When this link is moved around pivot point at A
angle FAb = angle BAC = angle BDC.

Link AB is a angle bisector of angle FAC.

You can see the process in animation

****** Kempe_6_rods_desc.dwg ******

To create this drawing and animation:
Then from command line, type 6_rods

Animation file creation:animation_6_rods

Kempe's Link is shown in the figure shown below.

Now there are 3 similar trapezoids,AHFG, AFCE and ACBD.
When this linkage is moved around the pivot A
angle HAF = angle FAC = angle CAB = (1/3) angle HAB

i.e., angle HAB is trisected by this linkage.

You can see the process in animation

****** Kempe_8_rods_desc.dwg ******

To create this drawing and animation:
Then from command line, type 8_rods

Animation file creation:animation_8_rods

Kempe's Link is shown in the figure shown below.

You can see the process in animation.animation

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

Animation file creation:animation_Kempe

#### Example Run: 105 degrees case:

---->input @4<105. -->105 degrees case

****** Kempe_trisection_105_deg.dwg ******

#### References

1. Robert C.Yates:"The Trisection problem",p 39 - 41

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