02.3 - Initial Kinematic Analysis

Ideal Motion Profile

Our robot is designed to row in the water. This means we need to have the paddle under water during the backstroke, and then out of the water during the forward stroke. The flatter the underwater portion, the better the performance. Any vertical movement is energy wasted on not moving the boat forward. Once the paddle is done with the backstroke, we want to ensure that the paddle remains above water to not impart any force in the wrong direction. To this end, the ideal path of the paddle is:

A flattened, long oval oriented parallel to the surface of the water
The bottom half of the motion is below water surface and should be as parallel to the water surface as possible
Top half of motion is above water surface, but can follow an arc

Mobility Calculation

Gruebler’s Equation:
- Number of Links: 4
- Number of 1 DOF Joints: 4
- Number of 2 DOF Joints: 0
- M = 3 (4 - 1) - 2 (4) - 0 = 1 DOF
Grashof Condition:
- L1 = 17.96mm, L2 = 53.88 mm, L3 = 50.8 mm, L4 = 50.8 mm
- S + L < P + Q
  - 53.88 + 17.96 = 71.84
  - 50.8 + 50.8 = 101.6
- -> 71.84 <101.6, L2 can rotate fully

Kinematic Analysis (position, velocity, acceleration)

Position analysis for one full rotation:

Figure 1. Plot of angular displacement of L3 and L4 vs input angle, theta 2, and position path of point p, which is joint connection between four-bar linkage and oar

Velocity for one full rotation

Figure 2. Velocity magnitude and velocity direction versus input angle, theta 2.

In Figure 2, it illustrates the velocity magnitude and direction of the connection point between output link 3 and the oar as functions of the input angle, through a full rotation of the input angle.

Figure 3. The angular velocity of the output link to the oar, omega 3, versus input angle, theta 2.

Figure 3 from above shows the angular velocity profile of output link 3 as a function of the input angle of the mechanism through a full rotation of the input angle.

Acceleration for one full rotation

Figure 4. The angular acceleration of the output link to the oar, omega 3, versus input angle, theta 2.

Mechanical Advantage vs Input Angle:

Figure 5. Mechanical advantage, MA, versus input angle, theta 2

The figure above illustrates the mechanical advantage of the system. The input force is assumed to be the torque of the input crank connecting the motor to the gears, and the output is the torque of the oars connection point to link 3.

Other Unique Features (Analysis)
Connection of oar to 4 bar mechanism (ball joint?) enables pivoting for 3D, non-planar motion
Custom joint connections (one piece pin + cap)

Animation for one full rotation

Video 1. The Animation of the first model attempt.

In the video shown above, we have linkages shown as solid lines and the velocity of each joint shown as dash line which visually present the absolute value of the velocity using its length.