#### Inverse Kinematics for a 2-Joint Robot Arm Using Geometry

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We revisit the simple 2-link planar robot and determine the inverse kinematic function using simple geometry and trigonometry.

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We revisit the simple 2-link planar robot and determine the inverse kinematic function using simple geometry and trigonometry.

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We discuss the structure of a right-handed 3D coordinate frame and the spatial relationship between its axes which is encoded in the right-hand rule.

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We extend the idea of relative pose, introduced in the last lecture, to 3D. We learn another right-hand rule that indicates the direction of rotation about an axis, and we see how we can attach 3D coordinate frames to objects to determine their pose in 3D space.

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We will introduce resolved-rate motion control which is a classical Jacobian-based scheme for moving the end-effector at a specified velocity without having to compute inverse kinematics.

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We learn how to describe the orientation of an object by a 2×2 rotation matrix which has some special properties. Try your hand at some online MATLAB problems. You’ll need to watch all the 2D “Spatial Maths” lessons to complete the problem set.

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We learn how to describe the 2D pose of an object by a 3×3 homogeneous transformation matrix which has a special structure. Try your hand at some online MATLAB problems. You’ll need to watch all the 2D “Spatial Maths” lessons to complete the problem set.

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MATLAB normally deals with matrices of floating point numbers. An image is typically represented by an array of small integer values, pixel value or greyscale values, which have a limited dynamic range and special rules for arithmetic.

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We resume our analysis of the 6-link robot Jacobian and focus on the rotational velocity part.

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The orientation of a body in 3D can also be described by a unit-Quaternion, an unusual but very useful mathematical object. In the MATLAB example starting at 3:48 I use the Quaternion class. For Toolbox version 10 (2017) please use UnitQuaternion instead.