Mobility Analysis:
Mobility analysis confirms the 5-bar mechanism has one degree of freedom (1 DOF). As seen in the figure above, the mechanism is comprised of five links, and has full joints at O2, A, B, C, and at the sliding contact between the slider (link 5) and the ground. O4 is a half joint. M = 3L - 2J1 - J2 - 3 = 3(5) - 2(5) - 1 - 3 = 1 DOFThis leads to the following relationship:
Kinematic Analysis:
The 5-bar mechanism can be broken into two separate vector loops - a 3-bar vector loop, and a 4-bar vector loop. The image below shows the first of these vector loops, Loop 1:
Vector analysis of Loop 1 yields the following position, velocity, and acceleration equations. Note that we assume the length of b is changing in this vector loop.
Position Equations:
Velocity Equations:
Acceleration Equations:
The next image is of Loop 2:
Vector analysis of Loop 2 yields the following position, velocity, and acceleration equations. Note that l7 and l3 are both changing length.
Position Equations:
Velocity Equations:
Acceleration Equations:
Computing these equations in MATLAB produces the following plots. Note, the input crank rotates 360 degrees at 10rpm (1.04 rad/s):
Plot 1: Link 3 position, angular velocity, and angular acceleration as a function of input crank angle.
Plot 2: Link 4 position, angular velocity, and angular acceleration as a function of input crank angle.
Plot 3: Slider longitudinal velocity and acceleration as a function of input crank angle.
Note, the slider achieves nearly constant velocity for roughly 180 degrees of input crank angle, followed by a quick reset to the home position.
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MATLAB animation of mechanism.