# lakehanne/screws

Of screws and rigid bodies and differential kinematic curves
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Failed to load latest commit information. Cuela ElasticTheory MurrayPkg wolfram_notes .gitignore PressurePsi.m README.md alpha_head.m alpha_iab.m bvp_free.m contact_kinematics.m cueto.m curvature_form.m isochoric_check.m psi_dot.m rodrigues.m rotz.m skewsem.m spherical_model.m spherical_model.m~ test.m trial.m twist.m twistmap.m

Some useful formulae in screw theory for robotics

• rodrigues: Given a vector, w, and an angle, theta, computes the exponential map of an angle using Rodrigues' formula. This is akin to the rigid body transformation of a body about an axis w, through a point q, by an angle theta.

• skewsem: Computes the antisymmetric or skew symmetric matrix from a 3D vector w = [wx, wy, wz].

• twist: Given an infinitesimal linear generator v and an infinitesimal angular generator w, computes the twist vector \in R^6 as [(-w x v) w]

• twistmap: Given a twist, \zeta, and an angle of rotation \theta, computes the exponential map of the twist exp(\hat{zeta}, theta), where $\hat{\zeta}$ is the isomorphism of the twist linear algebra in R^6

• curvature_form: Computes the relative curvature at the point of contact of two objects. This is typically useful in multifingered kinematics or IAB manipulations such as I used in my PhD thesis. This implementation is from Spivak's differential geometry book, 1979.

• psi_dot: computes the relative orientation between the tangent planes of two coordinate charts in R^2. The rotation angle through an angle \psi aligns the manipulating object's x-axis to the x-axis of the manipulated object. \psi is so chosen such that a rotation about the z-axis by \psi aligns the xy-axes of both objects (see Montana, 1988).

• contact_kinematics: A simple illustration of the contact dynamics between two rigid, or semi rigid objects in R^3. The examples assume that the objects are spheres with single coordinate charts as defined in [Murray, 1990].

• bvp_free: comptes the contact free boundary value deformation for a desired extension/compression of the SoRO model Result is the pressure

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