Quadruplanar inversor
The Quadruplanar inversor of Sylvester and Kempe is a generalization of Hart's inversor. Like Hart's inversor, is a mechanism that provides a perfect straight line motion without sliding guides. The mechanism was described in 1875 by James Joseph Sylvester in the journal Nature. Like Hart's inversor, it is based on an antiparallelogram but the rather than placing the fixed, input and output points on the sides (dividing them in fixed proportion so they are all similar), Sylvester recognized that the additional points could be displaced sideways off the sides, as long as they formed similar  triangles. Hart's original form is simply the degenerate case of triangles with altitude zero. Gallery. In these diagrams: Example 1 – Sylvester-Kempe Inversor. Example Dimensions: Cyan Links = formula_1 Pink Links = formula_1 Green Triangles: Shorter Sides = formula_3 Longest Side = formula_1 Yellow Triangles: Shorter Sides = formula_5 Longest Side = formula_6 Example 2 – Sylvester-Kempe Inversor. Example Dimensions: Cyan Links = formula_7 Pink Links = formula_7 Green Triangles: Shorter Sides = formula_1 Longest Side = formula_10 Yellow Triangles: Shorter Sides = formula_5 Longest Side = formula_6 Example 3 – Sylvester-Kempe Inversor. Example Dimensions: Cyan Links = formula_13  Pink Links = formula_13 Green Triangles: Shortest Side = formula_15 Intermediate Side = formula_13 Longest Side = formula_17 Yellow Triangles: Shortest Side = formula_18 Intermediate Side = formula_19 Longest Side = formula_20 Example 4 – Kumara-Kampling Inversor. Created by Fumio Imai and Arglin Kampling. Rather than having the third joint of each triangular link be displaced off to the side, the third joint can also be displaced collinear to the original links, allowing for the links to remain as bars. Example Dimensions: Cyan Links = formula_21 Pink Links = formula_21 Green Links = formula_23 Yellow Links = formula_24  Quadruplanar inversor