Everything 起来 does comes from one picture: standing up

Where the picture shows up in 起来

1. 1

   a body rising

   闹钟响了，快起来。

   nàozhōng xiǎng le, kuài qǐ lái

   The alarm went off — get up.

2. 2

   a sound rising

   孩子突然哭起来了。

   háizi tūrán kū qǐ lái le

   The child suddenly burst into tears.

   起来 marks not just the start but the start that keeps going.

3. 3

   gathered and stood up

   把桌上的东西收起来。

   bǎ zhuō shang de dōngxi shōu qǐ lái

   Put away the things on the desk, please.

4. 4

   a memory rising

   我想起来了，钥匙在包里。

   wǒ xiǎng qǐ lái le, yàoshi zài bāo li

   I remember now — the keys are in the bag.

5. 5

   rising to the senses

   这件衣服看起来很贵。

   zhè jiàn yīfu kàn qǐ lái hěn guì

   This jacket looks expensive.