Mechanism Mobility Calculation
- 6 links (L), 7 Full Joints (J1), 0 Half Joints (J2)
- M = 3L - 3 - 2J1 - J2 = 3(6) - 3 - 2(7) = 1 DOF
Position, Velocity and Acceleration Analysis
By varying Watt's original six-bar linkage, Mehdigholi and Akbarnejad created a 1 DOF walking mechanism that can be split into two sets: a 4-bar and 5-bar linkage. This separation is shown with two different highlights in the sketch below. Here, the four bar linkage is composed of links 1, 4, 5, and 3 but is not standard as it does not have two grounding points. In other words, it actually has two degrees of freedom, and requires a second system to restrict its position, velocity and acceleration. That role is fulfilled by conducting kinematic analysis on the five-bar mechanism of links 1', 3', 2, and 6 (ground). Because of this setup, the conventional method of analyzing a Watt's Six-Bar Linkage will not work–this mechanism is lacking one more grounding point for this methodology. Instead, seeing that theta 2 and 3' are unknowns in the 5-bar linkage and that they can be found using two equations (one real, one imaginary), allows me to then solve for the unknowns in the "four-bar" linkage of theta 4 and 5. (Note: All angles below are measured relative to the horizontal in a counterclockwise direction, as is set out by the convention established for this class.)
