Give it a shot. Generally, it's preferred that you try and post what you came up with as a jumping off point for discussion. People aren't going to jump in and do your job for you.
That said, it looks like a bunch of spheres attached to the outside of a cylinder with a rounded depression in the middle. All sounds fairly basic.
I agree with WarrenM, its better if you try something first, anything, but I can think of a few ideas to get you started.
1) Place one dumbbell on the surface of a sphere, align the pivot to the sphere and use the array tool, or just shift clone copies in rotation mode, hand placing each one. It's laborious but might be faster than trying to figure out another way.
2) Use particleFX to populate the surface of a sphere with the custom particle shape set to the dumbbell.
3) Use object painter to place the dumbbells on the surface of a sphere, either one click at a time or with some exact spacing. I forget if the standard object painter has one click placement, I think Soulburn Scripts does.
4) Use the Compound Object > Scatter to place dumbbells on the surface of a sphere, you might need to try various methods and different spheres, such as "scatter along face centers" on a geosphere or quad sphere, instead of a sphere with north and south poles.
5) Hunt around for spherical array methods and scripts, "superflow" comes to mind, its up on scriptspot.com
Keep in mind what is technically 'pure' isn't always the fastest and chasing technical purity can eat up a bunch of time so go with that gets it done in the shortest amount of time, unless you have time to experiment and just want to explore, then you can just go with whatever interests you.
Replies
That said, it looks like a bunch of spheres attached to the outside of a cylinder with a rounded depression in the middle. All sounds fairly basic.
1) Place one dumbbell on the surface of a sphere, align the pivot to the sphere and use the array tool, or just shift clone copies in rotation mode, hand placing each one. It's laborious but might be faster than trying to figure out another way.
2) Use particleFX to populate the surface of a sphere with the custom particle shape set to the dumbbell.
3) Use object painter to place the dumbbells on the surface of a sphere, either one click at a time or with some exact spacing. I forget if the standard object painter has one click placement, I think Soulburn Scripts does.
4) Use the Compound Object > Scatter to place dumbbells on the surface of a sphere, you might need to try various methods and different spheres, such as "scatter along face centers" on a geosphere or quad sphere, instead of a sphere with north and south poles.
5) Hunt around for spherical array methods and scripts, "superflow" comes to mind, its up on scriptspot.com
Keep in mind what is technically 'pure' isn't always the fastest and chasing technical purity can eat up a bunch of time so go with that gets it done in the shortest amount of time, unless you have time to experiment and just want to explore, then you can just go with whatever interests you.