3) Kinematic Analysis and Synthesis - Group 6

DOF of The System

From Gruebler’s equation, we can calculate the DOF of the system. The number of total links is 6. The linkage system has 7 full joints. Therefore, DOF=3*(6-1)-2*7=1.

Position and Velocity Analysis

1) Position Analysis

Figure 1. Hand calculation for position

2) Velocity Analysis

Figure 2. Hand calculation for velocity

Graphs and Analysis

Figure 3. Position of Point P W.R.T. Ground

Figure 4. X Position of Point P With Regards to Angle 2

Figure 5. Y Position of Point P With Regards to Angle 2

Figure 6. Angular Velocity of Link 5 W.R.T Angle 2

When observing Figure 3, it is helpful to note that the link system is oriented in a way that when the oar passes through a pivot, the graph with be inverted. Therefore, the top flat section of the position is the movement of the oar under the water. It is helpful to note that Figure 5 shows the height of Point P with regard to the input angle. By looking at Figure 3, you can determine a height that you would like to find the velocity of and use Figure 5 to determine the input angle at said point. Using the determined input angle, you can apply Figure 6 to find the velocity at the point. The two points presented in Figure 5 and Figure 6 showcase the ideal locations for the oar to enter and exit the water. Note that this section is the least steep, hence the acceleration at this interval is low compared to when the oar is out of the water.

Animation showing linkage

Below is a simulation of our linkage system that we modeled in PMKS. The red line in the video portrays the magnitude of instantaneous velocity at the point. The animation shows that the velocity is slower in the lower half(inside of the water) of the position and fast in the upper half(outside of the water).

Video 1. Animation showing linkage