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Screw theory is the algebraic calculation of pairs of vectors, also known as dual vectors [1] – such as angular and linear velocity, or forces and moments – that arise in the kinematics and dynamics of rigid bodies. [2] [3]
Traditionally the Newton–Euler equations is the grouping together of Euler's two laws of motion for a rigid body into a single equation with 6 components, using column vectors and matrices. These laws relate the motion of the center of gravity of a rigid body with the sum of forces and torques (or synonymously moments ) acting on the rigid body.
A screw displacement (also screw operation or rotary translation) is the composition of a rotation by an angle φ about an axis (called the screw axis) with a translation by a distance d along this axis. A positive rotation direction usually means one that corresponds to the translation direction by the right-hand rule. This means that if the ...
If the system is zero-force (torque only), it is termed a screw and is mathematically formulated as screw theory. [ 4 ] [ 5 ] The resultant force and torque on a rigid body obtained from a system of forces F i i=1,...,n, is simply the sum of the individual wrenches W i , that is
A screw axis.Mozzi–Chasles' theorem says that every Euclidean motion is a screw displacement along some screw axis.. In kinematics, Chasles' theorem, or Mozzi–Chasles' theorem, says that the most general rigid body displacement can be produced by a translation along a line (called its screw axis or Mozzi axis) followed (or preceded) by a rotation about an axis parallel to that line.
For each joint of the kinematic chain, an origin point q and an axis of action are selected for the zero configuration, using the coordinate frame of the base. In the case of a prismatic joint, the axis of action v is the vector along which the joint extends; in the case of a revolute joint, the axis of action ω the vector normal to the rotation.
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The general case of a rotating rigid body can be modeled using kinematic screw theory, which includes one axial vector, angular velocity Ω(t), and one polar vector, linear velocity v(t). From this, the angular acceleration is defined as