2142211 Dynamics NAV 1

Polar

Coordinates (r-θ)

2142211 Dynamics NAV 2

Position

Time derivative of unit vectors: and

Velocity

Acceleration

Special Case: Circular Motion

Examples

3. Polar Coordinates (r-θ)

2142211 Dynamics NAV 3

Applications

3. Polar Coordinates (r-θ)

2142211 Dynamics NAV 4

Position Vector

3. Polar Coordinates (r-θ)

2142211 Dynamics NAV 5

Velocity

3. Polar Coordinates (r-θ)

Time derivative of unit vectors

2142211 Dynamics NAV 6

3. Polar Coordinates (r-θ) Time derivative of unit vectors

2142211 Dynamics NAV 7

Velocity

3. Polar Coordinates (r-θ)

Acceleration

2142211 Dynamics NAV 8

3. Polar Coordinates (r-θ) Acceleration

2142211 Dynamics NAV 9

3. Polar Coordinates (r-θ) Circular Motion

2142211 Dynamics NAV 10

Example 1: Robot Arm

3. Polar Coordinates (r-θ)

Ans:

2142211 Dynamics NAV 11

Example 2: Hydraulic Cylinder

3. Polar Coordinates (r-θ)

Ans: -0.75 m/s, 7.5 rad/s, 9.74 m/s2,

65 rad/s2

2142211 Dynamics NAV 12

Example 3: Two links

3. Polar Coordinates (r-θ)

Ans: