Three Position Coordinated Motion Synthesis with a RRRP Mechanism
Schematic Diagram of a 4 Bar RRRP Linkage
In this experiment you will asked to design a RRRP mechanism whose input and output motion is coordinated at at least three given positions. That is, suppose the input link (link 2) is oriented at 30 degrees, the output link (slider) is required to have a displacement of 5 cm. Likewise, suppose the input link (link 2) is oriented at 45 degrees, the output link (slider) is required to have a displacement of 10 cm. Finally when the input link (link 2) is oriented at 60 degrees, the output link (slider) is required to have a displacement of 20 cm.Thus for an inital rotation of 15 degrees, there should be a displacement of 5 cm and for a further rotation of 15 degrees there should be an additional displacement of 10cm. Since we are concerned only about two pairs of positions, therefore it becomes a problem of coordinated two position synthesis. Such synthesis is also referred to as function snythesis. Why this is so is easily understandble, if you reframe the earlier problem in a different fashion, where we may seek the input angle (theta_2) to be 30 degrees, 45 degrees and 60 degrees, while the output displacement (s_4)s are 5+(30-30)/3, 5+(45-30)/3 and 5+(60-30)/3 respectively, thereby making s_4 (cm) = 5+{theta_2(degree)-30}/3 at three given orientations of the input link.
While such problems can be solved analytically, a graphical method of synthesis will be used here. Go to the Procedure Tab to see an animated guide to the geometrical constructions required. An animation of a sample 4 bar RRRP mechanism passing through 3 given sets of orientations can bee seen by clicking on the Demo Tab.