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This video introduces chapters 2 and 3 on configuration space, degrees of freedom, and rigid-body motions.

This video introduces the concepts of configuration, configuration space (C-space), and degrees of freedom, and describes a method for counting the degrees of freedom of a rigid-body in n dimensions.

This video describes common robot joints and derives Grubler’s formula for calculating the degrees of freedom of a mechanism.

This video introduces basic concepts in topology as applied to configuration spaces.

This video introduces representations of manifolds using minimum-coordinate explicit parametrizations and implicit representations, where the manifold is viewed as a surface embedded in a higher-dimensional space.

This video introduces holonomic configuration constraints, nonholonomic velocity constraints, and Pfaffian constraints.

This video introduces the task space, the space in which the robot’s task can most naturally be expressed, and the workspace, a characterization of the reachable configurations of the end-effector.

Autoplay of the YouTube playlist for all videos in this chapter.  This description box will not be updated with information about each video as the videos advance.

This video introduces rotation about an axis by the right-hand rule and right-handed frames, including the body frame and the space frame.

This video introduces the space of rotation matrices SO(3), a Lie group, and properties of rotation matrices.

This video introduces three common uses of rotation matrices: representing an orientation, changing the frame of reference of a vector or a frame, and rotating a vector or a frame.

This video introduces 3-vector angular velocities and the space of 3×3 skew-symmetric matrices called so(3), the Lie algebra of the Lie group SO(3). Any 3-vector angular velocity has a corresponding so(3) representation.

This video introduces the 3-vector exponential coordinates of rotation and the matrix exponential using the so(3) representation of exponential coordinates.

This video describes how the solution of a vector linear differential equation calculates the rotation achieved after rotating a given time at a constant angular velocity. The matrix exponential maps the so(3) matrix representation of the 3-vector of exponential coordinates of rotation to a rotation matrix in SO(3), and the matrix logarithm maps a rotation

This video introduces the 4×4 homogeneous transformation matrix representation of a rigid-body configuration and the special Euclidean group SE(3), the space of all transformation matrices. It also introduces three common uses of transformation matrices: representing a rigid-body configuration, changing the frame of reference of a frame or a vector, and displacing a frame or a

This video introduces the 6-vector twist, a representation of the linear and angular velocity of a rigid body. A twist can be represented as a normalized screw axis, a representation of the direction of the motion, multiplied by a scalar speed along the screw axis. A screw axis or twist can be represented in any