Selecting a gripper

1. Engineering problem

The gripper decides what the arm can pick. A parallel jaw suits rigid objects with parallel sides; vacuum suits flat, sealed surfaces; soft or adaptive fingers suit irregular objects. Whatever the type, the holding force must exceed the weight plus the inertia of the motion, with margin.

2. When is this needed?

• Selecting an end effector for a new application.
• When objects slip or are dropped.
• When the payload or speed increases.

3. Selection and design decisions

General characteristics (confirm on the datasheet of the gripper): parallel-jaw grippers have a stroke and a force and hold by friction; vacuum cups hold by pressure difference times area; soft and adaptive grippers conform to shape at lower precision. Friction grip needs normal force N such that μ·n·N ≥ m·(g + a)·SF, with friction coefficient μ, n contacts, mass m, acceleration a and safety factor SF; vacuum holding force is at best Δp·A per cup (a perfect seal): leaks and curvature reduce it.

4. Advantages and disadvantages

• Precision vs flexibility: jaws position objects accurately, adaptive fingers accept variation.
• Speed vs force: faster motion needs more holding force.
• Changeable fingers adapt one gripper to several parts.

5. Requirements and constraints

• Holding force with a safety factor of at least 2 for the worst object, friction and acceleration.
• Stroke or cup size covers the object range.
• Payload of the arm includes the gripper and the object.

6. Architecture

object properties (mass, size, surface) + motion (acceleration) ─▶ required holding force ─▶ gripper type and size ─▶ finger/cup design

7. Implementation

1. List the objects: mass, size, surface, tolerance.
2. Compute the required force for friction or vacuum (below).
3. Pick the type and the model from the datasheets.
4. Design the fingers or cups for the object.
5. Test with the worst object at the highest acceleration.

import math
G = 9.81
def friction_grip(mass, accel, mu, contacts, safety):
    need = mass * (G + accel) * safety        # total normal force summed over the contacts must resist weight plus acceleration
    return need / (mu * contacts)
def vacuum(mass, accel, cup_diameter_m, cups, vacuum_kpa, safety):
    area = math.pi * (cup_diameter_m / 2) ** 2
    holding = vacuum_kpa * 1000 * area * cups            # F = delta p * A, best case, perfect seal
    return holding, mass * (G + accel) * safety
f = friction_grip(1.0, 5.0, 0.4, 2, 2.0)
print(f"1 kg at 5 m/s^2, mu 0.4, two contacts, safety factor 2: each finger needs {f:.1f} N of normal force")
h, need = vacuum(1.0, 5.0, 0.040, 2, 60, 2.0)
print(f"vacuum, two 40 mm cups at 60 kPa: ideal hold {h:.0f} N against a requirement of {need:.1f} N -> {'ok' if h >= need else 'too small'} (real seals leak: derate)")
h2, need2 = vacuum(1.0, 5.0, 0.040, 2, 60, 2.0)
print(f"same cups on a porous surface leaking half the vacuum: {h2 / 2:.0f} N -> {'ok' if h2 / 2 >= need2 else 'too small'}")

Printed (checked by the site’s tests):

1 kg at 5 m/s^2, mu 0.4, two contacts, safety factor 2: each finger needs 37.0 N of normal force
vacuum, two 40 mm cups at 60 kPa: ideal hold 151 N against a requirement of 29.6 N -> ok (real seals leak: derate)
same cups on a porous surface leaking half the vacuum: 75 N -> ok

Reading it: a 1 kg object accelerated at 5 m/s² with μ = 0.4, two contacts and a safety factor of 2 needs about 37 N of normal force on each finger; two 40 mm vacuum cups at 60 kPa give an ideal 151 N against a requirement of 29.6 N, and still 75 N if half the vacuum is lost to leaks. All numbers are illustrative.

8. Real examples

• Warehouse box picking: vacuum cups sized with margin for leakage on cardboard.
• Machine tending: parallel-jaw gripper with custom fingers for a machined part.

9. Failure scenarios

• A gripper that holds the object statically and drops it during acceleration.
• Vacuum on a porous surface.
• Not including the gripper in the payload budget.

10. Troubleshooting

1. Measure the real friction coefficient with the object and finger material.
2. Check the vacuum level at the cup during motion.
3. Reduce acceleration to test whether force is the limit.

11. Validation

• The calculation prints the lines shown (executed by the site tests).
• The worst-case object survives repeated moves at the highest acceleration with margin.

12. Engineering checklist

• Objects listed
• Force with safety factor
• Stroke or cup size
• Payload with the gripper
• Finger or cup design
• Worst-case test

13. Further references

• Gripper datasheets for force, stroke, speed and mass; the force formulas are elementary mechanics and not drawn from one cited source.

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