Kinematic Analysis and Synthesis - JS

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 the sliding contact between the slider (link 5) and the ground. O₄ is a half joint. This 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.

MATLAB animation of mechanism.