有一位工程师甚至专门制造出一种机器，在下面一拉篮筐就能把球弹出来。
This is from the Standard Course Book of HSK5, section 13.
What is the meaning of 出来? To get out? Maybe a 取 is omitted? Something like 取出来? Or what?
Maybe all combinations are accepted: 把球弹出来 = 把球取出来 = 把球出来 = 把球弹取出来
?
弹 (tán , ㄊㄢˊ) is a verb, similar to 跳, that means "bunce". 弹出来 = bunce out.
It differs from 取 is that "弹出来" is getting the ball out by mechanical means; 取, take/get, is taking/getting the ball out manually.
One engineer even built a machine that would pop the ball out by pulling the basket underneath. 出来 is "out", not "get out". You don't need a 取 since there is already a 弹. You must and only choose one of "取" or "弹". They have the same function in the sentence.
To get out is “出”
“出来”is mean like that “get out there ”，“出去”is mean like that “get out here ”
You can think like this “出” then “来”。“something out a place where you are not”，then “something come to a place wehere you are。” the place like “space，spacial place，room，class，hall，Basket”
把球弹出来 = 把球取出来 = 把球出来 = 把球弹取出来, OK or not OK?
What I can say is that the following sentences are OK.
把球弹出来 = 把球给弹出来
把球取出来 = 把球给取出来
把 什么什么 给 做成 什么什么 结果。Here “把...给" is to put an objective in front of a verb to emphasize the objective. "给" is often omitted in this type of sentence.
Here "出" is not a verb as in 我出来 （I go out). As a whole, "出来" is an adverb that means a result of "outward". Therefore，把球出来 is not OK. In case you can not find an appropriate verb, use "弄" or "搞" as a universal verb as "do something" in English.
把球弹取出来, you have two verbs here "弹" (eject) and "取" (take), which is not OK.
If 把球弹取出来 means 把 球弹 取 出来 (把 球形的 炸弹 取 出来)， then it is OK. I do not think it fits the context here :-).
