• screw motion: a rigid body can be moved from any one position to any other by a movement consisting of rotation about a straight line followed by translation parallel to that line.
• twist
• wrench: Poinsot is credited with the discovery that any system of forces acting on a rigid body can be replaced by a single force applied along a line, combined with a torque about that same line.

• Rodrigues' formula

• pitch of the screw: the ratio of translation to rotation

• joint space Q

  • The joint space of a manipulator with p revolute joints and r prismatic joints is Q = T^p × R^r and has p + r degrees of freedom.

• base frame

• tool frame

• reference configuration

Relationship with Denavit-Hartenberg parameters

The workspace of a manipulator is defined as the set of all end-effector configurations which can be reached by some choice of joint angles.

• complete workspace
• reachable workspace (the set of positions (in R³) which can be reached by some choice of joint angles.)
• dextrous workspace

• smooth map
• diffeomorphism & diffeomorphic
• manifold of dimension n
• local coordinate charts
• smooth atlas & smooth manifold

• derivation
• tangent space & tangent vectors
• tangent map
• tangent bundle

// TODO