Even the best calculations can steer you wrong. Sometimes you just have to cut metal and see what happens.
For example, here is the original version of my garden tractor front loader:
Here is the redesign I came up with later:
Both versions used scrounged cylinders in nonstandard sizes. One has far fewer parts and weighs 70 lbs. less. This is also why I say sometimes you throw away half your materials. Sometimes whole parts of your design have to be cut off and set to one side.
70 lbs. at the far end of the loader boom makes a lot of difference to the operating performance of the machine. For both, the calculations on the range of motion and dump force on the actual bucket were correct. It is not always the things you measure and calculate that will be a problem, but aspects you did not even know to consider.
Sometimes what breaks won't even be on the parts you make. (my loader is now on a heavier tractor, and has had yet other things fixed and modified)
For straight out saving money and getting the job done, though, this was the actual best solution:
I finished building my machine because I am stubborn, and it was fun (for me, not everyone finds this type of design iteration work fun).
Have you had a chance to watch videos of people using a grapple to do what you are thinking of doing?