Robotic arm- Moment/bending moment/clamping force

[Aaron Mac]

Homework Statement:

Hello there, I'm currently designing a robotic arm, basically a revolute (shaft of rotating axis) and a prismatic joint (which further extends with the help of a motor), for which the necessary sizing has already been completed. As you can see, I previously created a counterweight to counteract the effect of the robotic arm's moment around the shaft while the gripper is holding something (payload) or even owing to the weight of the robotic arm itself. But, after some study, I discovered something called clamping force, which is utilized in the fastener industry, but I'm unable to make the required equations to establish the clamping force owing to my insufficient expertise in this area and maybe eliminating the counterweight. I'd appreciate it if someone could assist or guide me in this regard.

Relevant Equations:

Mass of link 1 - 0.8kg
length of link 1 - 0.15m

Mass of link 2 - 1kg
length of link 2 - 0.15m

Mass of payload - 0.3kg
Acceleration due to gravity in this case = 10ms^-2

Counterweight calculation
Moment around the axis of rotation = F*D
=(8*0.15) + (13*0.15)
= 3.15 Nm

 

[osilmag]

I think the clamping force would have to cause enough friction between the clamp and the rod to prevent sliding.

My LaTex isn't functioning right now, but I think it would be something like Fclamp * mu = mass * gravity.

 

[berkeman]

My LaTex isn't functioning right now, but I think it would be something like Fclamp * mu = mass * gravity.

$$\mu F_{clamp} = mg$$

 

[erobz]

You are trying to resist the torque of rotating a payload with the arm at the shaft that drives the arm, correct?

 

[Aaron Mac]

I think the clamping force would have to cause enough friction between the clamp and the rod to prevent sliding.

My LaTex isn't functioning right now, but I think it would be something like Fclamp * mu = mass * gravity.

Thank you very much. I have already chosen my screws and need to calculate according to this screw clamping force.

 

[Aaron Mac]

You are trying to resist the torque of rotating a payload with the arm at the shaft that drives the arm, correct?

No not really dear, it is the clamping force to resist deflection due to moment

 

[erobz]

No not really dear, it is the clamping force to resist deflection due to moment

I don’t get it. If you have already specified the fastener based on the design load, you’ve already specified the clamp force. In other words, specifying the bolt specifies the clamp force.

Your question seems odd to me, because the clamp force is what should be determined based off of the design load, and the appropriate fastener selected off of the clamp force required. You seem to be doing the process backwards if you have already selected the fastener as you indicate in post #5?

 

[erobz]

It's hard to tell from the picture, but I believe you are rotating the arm horizontally while it's carrying a load. The friction force at the shaft would have a very small moment arm. That torque is responsible for any angular acceleration the arm + payload experience around the axis of rotation (the shaft). The links and payload have moments of inertia about their own centers of mass, and they are compounded by the being at some distance from the center of rotation. Given the small moment arm of the applied force (from the clamping force of the collar) it's not clear to me which force is larger; simply supporting the weight of the arm and payload vertically, or the force involved in giving the system some modest angular acceleration?

$$ \frac{I_{tot} \alpha }{ r_{shaft}} \quad \text{or} \quad mg $$

In reality, fasteners are cheap, so you typically just select one that is obviously larger/stronger than necessary. Computing basic magnitudes might be more work than it's worth.