Overview

Master the mathematics that makes robot motion predictable, controllable, and verifiable. This rigorous, implementation minded reference develops robot kinematics from the ground up, starting with pose and rotation modeling in SO(3) and SE(3), then building to forward kinematics for serial chains, twist and screw formulations, and the differential tools used every day in modern robotics. You will move from clean, frame-consistent transformation algebra to Jacobians as true differential maps, with clear treatment of spatial versus body representations, adjoint transformations, and acceleration kinematics. Singularities are handled both geometrically and numerically, including rank tests, null spaces, SVD based conditioning, and manipulability measures that directly explain real performance limits. From there, the text connects theory to practice through inverse differential kinematics: pseudoinverse solutions, damped least squares for singularity robustness, weighting and metrics, redundancy resolution, null space projectors, and task priority methods. Constraint handling is covered with a modern optimization perspective, including inequality constrained formulations and quadratic programming approaches that naturally incorporate joint limits and feasibility. Every chapter includes multiple choice questions plus practice problems with fully explained answers to reinforce key derivations, expose common mistakes, and build the confidence needed to apply kinematic methods correctly on real mechanisms. What you will be able to do after working through this book Model rigid body poses and rotations with multiple interchangeable parameterizations Derive forward kinematics using Denavit-Hartenberg and Product of Exponentials methods Build and interpret manipulator Jacobians, including body and spatial forms Analyze and quantify singularities, near singular behavior, and dexterity limits Solve inverse differential kinematics for redundant robots with stability and robustness Apply task based and constrained IK methods using principled numerical tools Connect kinematic sensitivity to calibration and parameter identification

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