Solution for the gelsight_lab assignment

Just run ./examples/new_tracking_solution.py

Shear force visualization

Twist force visualization

Operation Demonstration

Calculating Real-World Displacement from GelSight Image Movement

To calculate how much a point on the image moves in real-world terms when it shifts by 10 pixels, we need to understand the relationship between the image's pixel dimensions and the real-world dimensions (Field of View).

Given GelSight Mini Specifications:

• Image Width (imgw): 320 pixels
• Image Height (imgh): 240 pixels
• Field of View (FOV): 18.6 mm (Horizontal) x 14.3 mm (Vertical)
• Movement: 10 pixels

For other specifications, refer to the GelSight Mini Product Sheet.

Steps:

1. Calculate the real-world size of one pixel:

text Horizontal size per pixel = 18.6 mm / 320 pixels = 0.058125 mm/pixel Vertical size per pixel = 14.3 mm / 240 pixels = 0.059583 mm/pixel

1. Calculate the real-world movement for 10 pixels:

text Horizontal movement = 10 pixels * 0.058125 mm/pixel = 0.58125 mm Vertical movement = 10 pixels * 0.059583 mm/pixel = 0.59583 mm

Thus, when a point on the image moves 10 pixels, it moves approximately 0.58125 mm horizontally and 0.59583 mm vertically in the real world.

Shear Force Estimation Method

The Simplified Shear Force Estimation Method calculates the force exerted on the skin when it undergoes displacement. This method uses the displacement, skin thickness, and the shear modulus to estimate the resulting shear force.

Definitions:

• Shear Strain (): Displacement per unit thickness of the skin layer:

text = x / d

where: - x is the displacement (in mm) - d is the thickness of the skin layer (in mm)

• Shear Stress (): Shear stress is related to shear strain using the shear modulus (G):

text = G * (x / d)

where: - G is the shear modulus (in Pa)

• Shear Force (F): Shear force is obtained by multiplying the shear stress by the contact area (A):

text F = G * (x / d) * A

where: - A is the contact area (in m)

Twist Force Estimation Method

The Simplified Twist Force Estimation Method estimates the force due to twisting or rotational displacement of the skin. This method uses the concept of torsional strain and torque.

Definitions:

• Torsional Strain (): Angular displacement per unit radius of the skin layer:

text = / r

where: - is the angular displacement (in radians) - r is the radius of the area being twisted (in meters)

• Torsional Stress (): Torsional stress is related to torsional strain using the torsional shear modulus (G):

text = G * ( / r)

where: - G is the torsional shear modulus (in Pa)

• Torque (T): Torque (or twist force) is calculated by multiplying the torsional stress by the moment of area (J):

text T = G * ( / r) * J

where: - J is the polar moment of inertia (in m), which depends on the geometry of the twisted area.

These simplified methods offer a foundational approach for estimating the mechanical interactions between the skin and external forces. They provide a basis for further refinement in experimental or more complex scenarios.