This open-access educational module covers the geometric kinematics, differential velocity mappings, and multi-body dynamic equations foundational to articulated robotic manipulators.
Core Technical Topics
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Forward Kinematics & Transformation Matrices: Denavit-Hartenberg (D-H) standard parameterization, homogeneous transformation decomposition into SO(3) direction cosine rotation matrices and translation vectors (T = [R, p; 0, 1]), and SE(3) frame composition.
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Inverse Kinematics & Solvers: Analytical closed-form solutions, kinematic redundancy resolution, and iterative numerical Newton-Raphson solvers utilizing the Moore-Penrose pseudo-inverse.
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Differential Kinematics & Jacobians: Geometric Jacobian column construction (linear and angular velocity mappings), static force-torque transmission duality via virtual work (tau = J^T F), kinematic singularity detection (det(J) = 0), and damped least-squares regularization.
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Multi-Body Manipulator Dynamics: Euler-Lagrange energy formulation (L = T - V), configuration-dependent symmetric positive-definite inertia matrix M(q), Christoffel-derived Coriolis and centrifugal effects C(q, q_dot)q_dot, conservative gravitational vectors G(q), and skew-symmetry passivity properties.
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Model-Based Motion Control: Computed torque control (feedback linearization), dynamic joint coupling compensation, and friction/backlash modeling.
Pedagogical Assets
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12 fully worked numerical engineering problems with complete mathematical derivations and step-by-step solutions.
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Dedicated engineering challenges analysis addressing kinematic singularities, payload mass parameter uncertainty, joint friction, and multi-axis inertial cross-coupling.
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Interactive conceptual quick reviews and self-assessment checkpoints.
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Standardized cross-platform layout designed for university coursework adoption and offline reference.
Target Audience & Level Designed for upper-division undergraduate engineering courses (Mechanical Engineering, Mechatronics, Robotics, and Control Engineering), advanced university-preparatory STEM programs, and robotics software/controls engineers.
