3. Kinematic Analysis and Synthesis - JP

Mobility analysis was conducted to ensure that the 6-bar window mechanism has one degree of freedom (1 DOF). As seen in Figure Afafafa, joints O2, O4, and A are pin joints while joints B and C are a combination of a pin joint and sliding joint. Each of these joints is a full joint, so there are a total of seven full joints and zero half joints. Therefore the mobility equation yields:

Figure 2: 6-Bar Window Mechanism Joints Labeled

Kinematic Analysis:

Using the geometry from the PMKS, the link lengths were obtainable and used for the positional, velocity, and acceleration analysis. The analysis was conducted using hand calculations.

The first vector loop analyzed consists of a three-bar vector loop consisting of the input crank and sliding joint B.

Figure 3: Vector Loop 1

Vector analysis shows that vector equation is:

Position Equations:

Velocity Equations:

Acceleration Equations

The next vector loop consists of the second slider joint and vector loop equation:

Figure 4: Vector Loop 2

Position Equations:

Velocity Equations:

Acceleration Equations:

Note:

The carrots above the variables signify the derivative of the variable (one carrot = 1st derivative, two carrots = 2nd derivative)

O2A=6.575 in

AB=4.956 in

O4B=5.088 in

O4C=16.41476 in

BA=AB=4.95535 in

thetaO4O2=theta1=33.0205 deg

O4O2=7.951338 in

Inserting these equations into MATLAB to solve produces the following plots (Note. the input crank rotates from 131.1541 to 228.8145 degrees, which was found from the PMKS data, and the input crank rotates at 10 rpm=1.047rad/s):

Figure 5: Figures Obtained from Analytical Equations in MATLAB

The analytical equations were compared to the data obtained from the PMKS, specifically the acceleration data. The figures below show the acceleration data from PMKS:

Figure 6: Figures Obtained from PMKS Data Set in MATLAB

The figures compared to that from the analytical equations do not match. So there might be a mistake with either the equations or the MATLAB code.