Notes in Week 3 - Forward and Inverse Kinematics

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Status	Last Update	Fields
Published	10/15/2024	The {{c1::Jacobian matrix}} maps joint velocities to end-effector velocities in both forward and inverse kinematics.
Published	10/15/2024	{{c1::Forward kinematics}} is concerned with determining the position and orientation of the end-effector based on the given joint parameters.
Published	10/15/2024	In kinematic chains, each joint is assumed to have {{c1::one degree of freedom}}, such as a revolute or prismatic joint.
Published	10/15/2024	The position and orientation of the end-effector in the inertial frame are given by the product of {{c1::homogeneous transformation matrices}} for eac…
Published	10/15/2024	A {{c1::revolute joint}} describes rotational movement, whereas a {{c2::prismatic joint}} describes linear movement.
Published	10/15/2024	The {{c1::Denavit-Hartenberg (DH) convention}} is a standard method for assigning coordinate frames to links in a manipulator to simplify kinematic ca…
Published	10/15/2024	The DH parameters consist of four variables: {{c1::link length (\(a\))}}, {{c2::link twist (\(\alpha\))}}, {{c3::link offset (\(d\))}}, and {{c4::join…
Published	10/15/2024	The forward kinematics problem always has a {{c1::unique solution}}, meaning that the end-effector's position and orientation can always be calculated…
Published	10/15/2024	The homogeneous transformation matrix \( T \) is used to represent both {{c1::rotation}} and {{c2::translation}} of links in a single matrix.
Published	10/15/2024	The transformation matrix is the product of four transformations: {{c1::rotation about the z-axis}}, {{c2::translation along the z-axis}}, {{c3::trans…
Published	10/15/2024	The end-effector's position and orientation relative to the base frame can be expressed as the product of transformation matrices: {{c1::\( T = A_1 A_…
Published	10/15/2024	Unlike forward kinematics, the inverse kinematics problem may have {{c1::no solution}}, {{c2::one solution}}, or {{c3::multiple solutions}}.
Published	10/15/2024	The inverse kinematics equation is typically written as \( T(q_1, q_2, \dots, q_n) = H \), where \( H \) represents the desired {{c1::end-effector pos…
Published	10/15/2024	The Denavit-Hartenberg transformation matrix, \( A_i \), plays a key role in solving the inverse kinematics for each joint's {{c1::angle}} or {{c2::di…
Published	10/15/2024	The inverse kinematics problem for a 6-DOF manipulator can be decoupled into two simpler problems: {{c1::inverse position kinematics}} and {{c2::inver…
Published	10/15/2024	For manipulators with a {{c1::spherical wrist}}, the inverse kinematics problem can be simplified by first finding the position of the {{c2::wrist cen…
Published	10/15/2024	The {{c1::geometric approach}} to inverse kinematics involves projecting the manipulator onto a plane and solving for joint angles using {{c2::trigono…
Published	10/15/2024	In a {{c1::3P (PPP) Cartesian manipulator}}, the inverse kinematics problem is simplified as the joint variables directly correspond to the Cartesian …
Published	10/15/2024	The {{c1::Jacobian inverse method}} and the {{c2::Jacobian transpose method}} are two numerical techniques for solving inverse kinematics iteratively.
Published	10/15/2024	The {{c1::Newton-Raphson method}} is commonly used to iteratively solve for joint angles in inverse kinematics problems.
Published	10/15/2024	The {{c1::Jacobian matrix}} maps joint velocities to end-effector velocities in both forward and inverse kinematics.
Published	10/15/2024	The {{c1::Jacobian inverse}} is used to calculate joint velocities given end-effector velocities in kinematic analysis.
Published	10/15/2024	In forward kinematics, the {{c1::position}} and {{c2::orientation}} of the end-effector are calculated using the robot's joint angles and link lengths…
Published	10/15/2024	The Denavit-Hartenberg (DH) convention uses {{c1::four parameters}} to describe each link and joint in a robotic manipulator.
Published	10/15/2024	The homogeneous transformation matrix \( T \) represents both {{c1::rotation}} and {{c2::translation}} in robotic kinematics.
Published	10/15/2024	The end-effector's pose is determined by multiplying the transformation matrices of each {{c1::joint}} and {{c2::link}} in the robotic chain.
Published	10/15/2024	The forward kinematics problem always has a {{c1::unique solution}}, making it easier to solve compared to inverse kinematics.
Published	10/15/2024	A {{c1::prismatic joint}} allows linear motion, while a {{c2::revolute joint}} allows rotational motion in a kinematic chain.
Published	10/15/2024	For a planar two-link manipulator, the end-effector position is computed using {{c1::trigonometric functions}} like sine and cosine.
Published	10/15/2024	The {{c1::forward kinematics equation}} provides the relationship between joint variables and the position/orientation of the end-effector.
Published	10/15/2024	{{c1::Inverse kinematics}} determines the joint variables needed to place the end-effector in a desired position and orientation.
Published	10/15/2024	In inverse kinematics, the {{c1::Jacobian matrix}} is used to compute the necessary joint velocities for a given end-effector velocity.
Published	10/15/2024	For robots with redundant degrees of freedom, multiple inverse kinematics solutions exist, requiring a {{c1::redundancy resolution}} strategy.
Published	10/15/2024	In a {{c1::spherical wrist}} configuration, inverse kinematics can be simplified by decoupling position and orientation calculations.
Published	10/15/2024	The {{c1::Jacobian transpose method}} is another approach for solving inverse kinematics, mapping task-space velocities back to joint velocities.
Published	10/15/2024	When solving inverse kinematics numerically, good {{c1::initial guesses}} for joint angles can speed up convergence.
Published	10/15/2024	Inverse kinematics solutions for a 6-DOF robot can be divided into solving for {{c1::position}} and {{c2::orientation}} separately.
Published	10/15/2024	The {{c1::Jacobian pseudoinverse}} is used to compute approximate solutions to inverse kinematics problems when the system is near singularities.
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