## Determining the deflection of a support rod during acceleration

Hi all,

I'm currently designing a housing for a camera and omnidirectional mirror for a robot. The housing is connected to the robot through a rod of about 25mm diameter.
....{...}.... (housing)
......|...... (rod)
...(___)... (robot base)

I'm trying to compute the deflection in the rod when the robot accelerates (or deccelerates) at its max of 1m/s^2 but not sure how I'd go about it.

Conceptually, when the robot is at rest the rod would act as a column with a concentric load. Once the robot accelerates, the inertia of the rod and housing would cause it to want to stay, hence causing the deflection. Once it begins to deflect, the housing becomes an eccentric load and causes the rod to deflect more. The dimension of the rod is fixed so I have to ensure the housing is light enough to minimise deflection and vibration.

At this stage I'm looking at doing a rough FEA simulation and seeing what numbers it spits out but how would you go about solving such a problem analytically?
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 Blog Entries: 2 Recognitions: Gold Member Science Advisor Just consider the rod to be a cantilever beam with a force at the end of it, and calculate the maximum deflection based on the acceleration force on the camera. http://www.efunda.com/formulae/solid...cantilever.cfm
 Is it really that simple? The base of the robot is what's accelerating, not the camera (housing). I guess we can use the robot as the reference frame and take the base of the rod to be fixed, with the housing accelerating, however will modelling the dynamic system as static be a reasonable approximation? Also, given the housing + components is relatively heavy (1-2kg), surely the axial load cannot be ignored? Once the rod starts to deflect, it'll become a pretty significant eccentric load.

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## Determining the deflection of a support rod during acceleration

Looking at it in the static case is a good start in my opinion, and you can increase complexity with a dynamic analysis if your findings make it seem necessary.

Making assumptions to simplify your analysis is engineering 101, but only you can decide "what's necessary." Step 1 is to put bounds on how much your beam will deflect so you can decide what else might contribute to the design problem.
 You are way overthinking this. You've got a mass (1-2 kg) at the end of a rod. They are connected, so if the robot accelerates, so does the mass (they are connected after all). You are correct in that the inertia of the mass will mean it wants to resist that acceleration. That's why F=m*a. Hence the deflection. Unless your rod is so undersized that the thing actually bends, I don't think you'll have to care as much about the axial loading. The bending (and the uplift at the connecting rod mounting point) will be your most significant loads.
 Blog Entries: 2 Recognitions: Gold Member Science Advisor You also might calculate the first mode of virbration for the beam/mass, because that number will give you some insight into how stiff it is and how it will hold up to acceleration applied over a certain time constant.
 Have always struggled reducing a real world mechanical problem down to a simple model. Working on it... Just to clarify with a FBD of the external forces: However, assuming that the column isn't gonna buckle under the load (not gonna happen), the bending caused by the axial force is relatively minor compared to that caused by the acceleration, due to the much smaller moment arm, therefore Fy can be disregarded.

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