A "Link" is a special bond Emerl forms with someone who has amazing power. The Gizoid, Emerl, first formed a Link with Gerald Robotnik over 50 years ago.
List of Emerl's Links
After saying, "Show me your power. Or I shall not obey. I represent all things and shall become Gizoid, the conqueror of all." Gerald then brought out his collection of guns, and fired them all to show the Gizoid that power. Seeing this power, Emerl formed a Link with Gerald and followed him everywhere and not talking to anyone else. But the government became wary of Project Shadow, so the professor gave Emerl to the government to buy some time and warned them not to experiment weapons with him. But they didn't listen and Emerl absorbed the weapons, which caused a massive explosion. This caused the government to shut down Space Colony ARK and cease all research, killing almost everyone on the ARK. Emerl was then put in stasis for 50 years until he was discovered by the professor's grandson.
After Emerl didn't respond to Eggman's orders, he threw Emerl out and Sonic found him at Emerald Beach. When Sonic found him, Emerl said "Show... power... OR I sh...all ob...ey... Sha...ll conqu...r a...ll...". The blue hedgehog then showed off some lightning fast moves and Emerl said that he will not leave Sonic's side. Sonic then takes the old Gizoid to Tails to fix him up but was caught by Shadow. Sonic defeated Shadow and the black hedgehog left. It was then discovered that Emerl grows stronger and smarter with each Chaos Emerald. The three then go to Knuckles' to get a Chaos Emerald but Knuckles thinks Emerl is one of those robots from the news and attacks Emerl. After defeating the echidna, Knuckles gives Sonic and Tails an Emerald and they give it to Emerl, who says "thank you".
Although the Gizoid can only establish a link with one person at a time, Emerl will take orders from anyone else if permission is granted by its master, during the course of Sonic Battle, Sonic allows Emerl to take orders from other playable characters; he allows Emerl to accompany Tails in order to discover Emerl's origins at the library at Central City. Later, Sonic allows Rouge to order Emerl after she complains that Emerl keeps ignoring her, although later it is revealed that she wanted possession of Emerl so she could train it to become the "ultimate jewel thief". After freaking out when he sees Amy approaching, Sonic told Emerl to obey Amy, Amy and Emerl then establish and mother-son relationship after Amy misinterpreted Emerl's purpose when she talked to Tails. Later, Sonic allows Knuckles to order Emerl so that Knuckles can further his training. Lastly, during Shadow's chapter, Shadow states that he has his own link with Emerl, as he believes them both to be nothing more than weapons created to destroy. After stating this, Sonic orders Emerl to follow Shadow, so that he could uncover more of his and Shadow's past whilst on the Ark.
In Emerl's chapter, Eggman reveals one final link that Emerl has in his programming which was made by a scientist on board the Ark after Gerald had no choice but to hand the Gizoid over to the government. This program allows Emerl to re-establish a link if it's shown overwhelming power. Eggman was able to display such power by firing his Final Egg Blaster into a distant star, destroying it. However, as Emerl had been awakened with all seven Chaos Emeralds, Emerl reverted to his destructing nature, which ultimately lead to his destruction at the hands of Sonic.