ME321 – Kinematics and Dynamics of Machines Introduction (Continued) Steve Lambert Mechanical Engineering, U of Waterloo 12/7/2018

Simple Mechanisms – 2 links Consider 2 links: M = 3(2-1) = 3 A single pin or slider joint (or 2 roll-sliding joints) can reduce the mechanism to 1 dof not very useful 1 2 1 2 12/7/2018

Simple Mechanisms – 3 links Consider 3 links: M = 3(3-1) = 6 2 pin/slider joints plus 1 roll-sliding joint are necessary to limit it to 1 dof Useful as cam mechanisms 1 2 3 1 1 2 3 12/7/2018

Four-Bar Mechanisms 4 links and 4 pins/sliders gives M = 3(4-1) - 2(4) = 1 dof This is a particularly useful mechanism 1 1 2 3 4 1 1 2 3 4 12/7/2018

Four-bar mechanisms By extending the coupler, a four-bar mechanism can be used to generate a wide variety of functions 1 1 2 4 3 Coupler curve (artist’s impression) 12/7/2018

Six-Bar Linkages Six bars and 7 pin/slider joints give M = 3(6-1) - 2(7) = 1 dof However, now at least 2 links must be ternary For a Watt linkage, the two ternary links are adjacent 1 1 Watt I 2 3 5 6 4 1 1 1 Watt II 2 3 4 5 6 12/7/2018

Six-Bar Linkages For a Stephenson linkage, the 2 ternary links are separated by a binary link 1 1 Stephenson II 2 3 4 6 5 1 1 Stephenson I 2 3 4 5 6 12/7/2018

Six-Bar Linkages 1 1 1 Stephenson III 2 3 4 5 6 12/7/2018