Robotic arms and grippers

How can I make my robot lift blocks if I am not allowed to use any readymade mechanical gripper?

If you cannot purchase something, then you will need to design and create it yourself.
Perhaps use other grippers and systems as inspiration.

What do you mean by other grippers and systems?

See how other companies have designed their grippers:
robotshop.com/en/catalogsear … t&dir=desc