After the recent announcement of complex organics being found on Mars within the curiosity rover's meager 5cm drill depth, I had an idea about artificially increasing it:

Is curiosity rover's arm strong enough that it would be able to flip a small to medium sized rock over?

Would such a rock flipping operation reveal an area of scientific interest as the area underneath is presumably more sheltered from solar radiation?

Has a rock flipping operation been suggested or used before?

  • $\begingroup$ Bonus idea: Maybe when you flip the rock, unique dust is kicked up or gas/moisture escapes. These could be measured with atmospheric sensors. $\endgroup$ – Dragongeek Jun 8 '18 at 18:22
  • $\begingroup$ To measure escaping gas or moisture would be very difficult. There is too much space for the molecules to spread. Gas or moisture had a very, very long time to escape before the rock was flipped. $\endgroup$ – Uwe Jun 11 '18 at 18:20

This took a fair bit of investigation!

Arm Strength

The Mars Science Laboratory Robotic Arm (RA) is 2.2m in length, is made of two arm sections (an upper arm and a forearm) and is controlled by 5 actuators. These consist of (among other things) a brushless DC motor and a planetary gearbox to step down the motor speed and increase torque.

Two of these actuators have a vertical pivot axis and control the azimuth (pan) of the arm - one at the shoulder and one at the wrist. The other three actuators have horizontal pivot axes and control the elevation (tilt) - at the shoulder, elbow and wrist.

Annotated photograph of the Robotic Arm showing instrument turret and joint actuators

In order to work out whether we can start rock-flipping, we need to calculate the size of the force the RA can apply at its far end. If we only consider a vertical lifting force, I believe we can neglect the azimuth pivots and assume that the elevation actuators will be the limiting factor. The arms sections were torsion tested to withstand the loads of operation.

We also need to take into account the mass distribution of the arm and the attached instruments to figure out how much more additional weight the arm could lift.

It is clear that the wrist elevation actuator will experience the smallest moment and the shoulder actuator the largest, with the elbow somewhere in between. Because of this, we can focus solely on the capability of the shoulder elevation actuator (SEA).

The SEA is a Low Power High Torque Actuator (LPHTA) capable of producing 1143Nm of torque at 0.532RPM from a 4000RPM motor and a gearing ratio of 7520.

Arm Mass

The mass distribution is difficult to calculate and some estimates have been made:

The mass of the entire arm (excluding the instruments) is 67kg. At least 16kg of this mass is situated at the SEA and therefore applies no torque, leaving ~50kg to account for. The Turret Structure at the end of the RA has a mass of at least 10kg and the elbow actuator ~8kg, leaving ~33kg for the arm sections and other components.

The instruments are contained in the Turret Structure and have a combined mass of 34kg.

Worst case - fully extended arm

Our mass distribution is as follows:

  • 44kg at 2.2m (Turret and instruments)
  • 8kg at 1.1m (Elbow actuator)
  • 33kg at 1.1m (Remaining mass, approximated to be at halfway)

Using Martian surface gravity 3.711$ms^{2}$, the torque is easily calculated from:

$$\sum_{i} \boldsymbol{r_{i}} \times \boldsymbol{F_{i}}$$

giving a torque magnitude of 527Nm.

This leaves us with 616Nm to play with which corresponds to a lifting force at the end of the arm of ~280N. This is consistent with the RA's requirement to preload the sample acquisition drill with 300N.

What does 280N get us? A surprising amount!

In Martian gravity, this allows us to entirely lift a 75kg rock which I would definitely classify as 'medium sized'. If we only want to pivot the rock to flip it, the lever would approximately double that to ~150kg. If we shorten the arm and lift a rock closer to the rover, this number is increased even further.

Notes and Limitations

  • I have clearly taken some liberties with the numbers on mass distribution.
  • The fact that the Turret houses four very delicate scientific instruments would make it both difficult and undesirable to use it for lifting purposes.
  • I haven't taken the stability of the rover into account, but I assume this is far from a limiting factor for a 1 ton rover.
  • I've spent too long investigating this and there's probably a simple source somewhere that I've missed that does all the calculations for me!

I haven't been able to find any information on whether this procedure has been suggested, but given the points made above, I assume not.

References that I used widely 1, 2, 3.

Radiation Shielding

Our 75kg rock (if made from something similar to basalt) is approximately 40cm in size. This provides some shielding as discussed here, but after several million years undisturbed on the surface, I doubt this will make any significant difference. More significant may be the shelter from Martian weather, giving the regolith material beneath it a different distribution to surrounding areas.

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    $\begingroup$ Hopefully my maths and conclusions are correct, but please do check and let me know if I've made any glaring mistakes. $\endgroup$ – Jack Jun 12 '18 at 14:56
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    $\begingroup$ Glaring mistakes he says, approximations on this question were beyond what I'd expect! Nice answer man. $\endgroup$ – Magic Octopus Urn Jun 12 '18 at 18:28
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    $\begingroup$ This is exactly what I was looking for! Now that we know we can do it, I wonder if we should do it... $\endgroup$ – Dragongeek Jun 13 '18 at 8:10

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