What you are picking up decides the mechanism. This guide sorts the options by the objects they handle and lists the parts for each.
Two jaws closing on a common axis. Predictable, easy to model, and it drops anything that is not roughly prismatic. Grip force comes from the actuator and the mechanical advantage of the linkage, so a small servo with a good linkage beats a large servo with a poor one.
Assembly
A vacuum cup handles flat, smooth and light objects better than any jaw, and it fails completely on anything porous or textured. The pump is the noisy, power-hungry part of the system and it runs whenever the object is held.
Underactuated fingers wrap around whatever they touch, driven by one actuator through a tendon or a linkage. They handle variety without any perception at all, which is their real advantage, and they hold less firmly than a parallel jaw at equal actuator size.
Without feedback the gripper cannot tell a successful grasp from a closed empty hand. A force sensing resistor on the jaw face is the cheapest answer and reports contact rather than force. Reading the actuator current is free and reports load rather than contact.
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