Lecture 20 Elliptical Trammel : 3rd Inversion of variation of Crank - Slider Mechanism OR Double Slider Mechanism ( Slider - Slider Mechanism) with Double Slider as Fixed Link (Slotted Frame)

Link 3 = Double Slider (Originally Coupler) as  Fixed Link (Slotted frame)

Input Link = Link 2= 2nd slider/(Originally Crank) 

Link 1 = Conecting link between two sliders (Originally Frame) as Coupler Link

Follower Link = Link 4 = 1st Slider / (Originally Slider)

Consider a four link planar mechanism wherein link 1 has two revolute pairs at it's either ends, link number 2 has a revolute pair at R2 with link 1 and a prismatic pair at P3 with link 3 along the vertical direction and, similarly, link 4 has a revolute pair at R1 with 1 and a prismatic pair at P4 with link 3 in the horizontal direction. Here the two prismatic pairs (P3 & P4) have an angle of 90° between them. 

In elliptical trammel mechanism, link 3 (Double Slider) that has prismatic pair at both the ends is made stationary / fixed.  This coupler link / Double Slider  (link-3) has a prismatic pair at P4 with Original Slider (link-4) in horizontal direction and a prismatic pair at P3 with Original Crank (link-2) that goes to Infinity / 2nd slider that slides in vertical direction ( a direction at right angles to that of the horizontal direction).  

The connecting link between two sliders, namely, the rod ABCD has revolute pair R1 with the Original Slider (1st Slider) at C and another revolute pair R2 with 2nd Slider ( Originally Crank)  at A. Any point on the extended  link R2R1 (that is , extended connecting link between two sliders) that connects 2nd Slider / originally crank at infinity (link-2) and 1st slider / original slider (link-4) will trace out an ellipse as the original 1st Slider (link-4) and originally crank at infinity / 2nd slider slide , respectively, in horizontal slot and vertical slot in link-1 (Slotted Frame). 

To summarize , third inversion of RRPP ( 2R-2P ) mechanism yields mechanism of elliptic trammel, in which link - 3 is fixed. Any point D on  link - 1       [Extended Coupler Link / Motion Transfer Link] describes an ellipse as it moves. The midpoint B of AC will obviously describe a circle. The point A generates a vertical straight line because of prismatic pair at P3. Similarly, the point C generates a horizontal straight line because of horizontal prismatic pair at P4. The three exceptions exhibited by points A, C and midpoint B are nothing but degenerated cases of the same ellipse from elliptical trammel.

Study Guide for Four-Link Planar Mechanisms

Quiz: Short-Answer Questions

Answer the following question in 2-3 sentences each, based on the provided source material.

5. Why is the Elliptic Trammel so named, and what other geometric shapes can be generated by specific points on its moving rod?

Answer Key

5. The mechanism is called an Elliptic Trammel because a point (D) on its moving rod traces a perfect ellipse as the rod moves. Other points on the same rod can generate different shapes; points A and C, which are connected to blocks in the prismatic slots, generate vertical and horizontal straight lines, respectively, while the midpoint between A and C generates a circle.