Well one thing's for sure...I know this question came from a human, because a cat would never complain about this.
The scratches on your arms reflect the million years or so of evolution looking out from behind a cat's eyes. In cat culture, claws and teeth deliver cattishly affectionate embraces....or they can serve as lethal weapons.
When humans roam outside their species for companionship, they have to realize that the things that are pleasureable to other species may be painful to the human. It would be wise to remember that in all things.
First you have to start with the fact that cats have a sturdy top layer of hair (fur) while humans have only a light layer of hair. But the skin underneath this top layer is different too. Human skin is relatively tender, and highly charged with nerve clusters that signal pain, pressure and temperature. Cat skin has a different arrangment of nerves, making a cat's brain interpret bits and scratches very differently from how a human brain would interpret them.
For example, in cat courtship, there is often a period of swatting between the tomcat and the "queen" cat, often with claws out. The pricks of this mutual clawing stimulate the cats to take things up a notch including the tomcat planting a big ole forceful bite to the queen cat's neck. Although this bite applied to a human neck would have you humans howling in pain, the queen cat tolerates it and derives pleasure from it.
Within the cat's brain there are links between a pleasure sensation...such as the delightful sensation of fingers running through soft cat fur...and the actions that accompany other pleasure sensations, such as clawing and biting.
If you pet your cat long enough, it can trigger the cat to respond in a frenzy of swats and what we like to call "love bites." To him, this is just a natural thing to do. To you, a human, it's a session of petting your cat morphing into a lapful of teeth and claws...ouch.
The good news is that you can usually diminish the behavior through some training. Part of the training is disciplining yourself to stay alert when petting him so you can recognize his body signals and know when to stop. Stop petting him BEFORE he starts getting too restless and frisky. A real simple body signal to watch for is the tail. When it starts twitching and thumping around, he's getting ready to be a little wild.
The other part of the training is reinforcing his good behavior with praise rather than pats and strokes. If he's on your lap, talk to him in soothing, loving tones instead of petting him. We cats LOVE to be talked to; we don't know every word being said, but we sure know tone of voice. With time, your cat will learn that you...and your lap...are no place for him to let his wild side out.