Lesson 05 · Book chapter pointer
Grasping
Read the chapter source: grasping.tex — do not treat this note as the book.
Learning goals
- Describe a grasp as a set of contacts, not as a pretty photo of a hand.
- Contrast form closure and force closure in one sentence each.
- Name what a contact model is allowed to transmit (normal, friction, moment).
- Explain why more fingers are not automatically a better grasp.
- Connect grasp quality to task wrenches, not to aesthetics.
Teaching note
Grasping is applied statics with social pressure. Everyone has seen a robot hand fail to pick up a water bottle; fewer people can say whether the failure was geometry, friction, or a wrist that could not resist a torque. Start by counting contacts. Each contact is a little machine that can push, maybe rub, almost never pull. The grasp is the union of those machines. If they cannot resist the wrenches the task will apply — gravity, a twist of a lid, a shove from a human — the grasp is a handshake, not a fixture.
Form closure is the purely geometric version: the contacts lock the object even with no friction, like a puzzle piece in a well. Force closure allows friction and bounded actuator effort to resist wrenches. Classroom objects split cleanly. A coin on a table is not form-closed by the table. A nut on a well-fit wrench is trying to be. Most gripper demos are force-closure stories that die when the object is oily or the fingers hit at a bad angle.
Contact models are where you admit ignorance. A frictionless point contact only pushes along the normal. A frictional point contact adds a shear inside the cone. A soft finger may resist a moment about the normal. Soft-finger models make some grasps look possible that a steel point would drop. Choose the model that matches the hardware, then stay loyal to it when you compute.
Quality metrics try to score a grasp: how large a wrench can you resist, how even is the load, how far are you from losing a contact. They are useful and they lie. A “high quality” grasp that collides with the table is not a grasp. A “low quality” power grasp that swallows the object may be what the warehouse wants. Always name the task wrench you care about — lift, insert, or hold still while someone tugs.
If you have no hand in the lab, use two rigid fingers and a block. Mark contact points, draw cones, and ask whether gravity is inside the cone sum. Then tilt the table. That one experiment teaches more than a week of gripper catalogs. Read the book chapter for the careful definitions and the examples this note is only allowed to point at.
If \(G\) maps contact wrenches \(\lambda\) to the object wrench, force closure asks whether the equations \(G\lambda + w_\text{ext}=0\) have a feasible \(\lambda\) inside the contact cones.