Robotics: Fundamentals and Kinematic Modeling (Part 1)

Explore robotics as an interdisciplinary field that designs, builds, and operates robots across manufacturing, agriculture, medicine, and surveillance, blending mechanical, electrical, computer science, and artificial intelligence principles including kinematics.

Differentiate robot from manipulator: a robot is an autonomous or semi-autonomous computer system with mobility and sensing, while a manipulator is a non-mobile arm with joints and end effectors.

Explore robot configurations used in industry, from cartesian and cylindrical to spherical, articulated, scara, and delta, detailing joints, degrees of freedom, and motion types.

Learn about joint types in manipulators, including revolute (R) and prismatic (P) joints with one degree of freedom, plus examples like elbows, telescopic arms, and robotic wrists.

Identify the difference between active joints driven by actuators and passive joints moved by external forces, with active joints powered by servo or stepper motors and passive joints like hinges.

Explore key terminologies defining robot capabilities and limitations, including payload capacity, degrees of freedom, reach, accuracy, repeatability, end effector, workspace, speed, sensors, actuators, and control systems.

Compare open-loop stepper motors with no feedback to closed-loop servo motors with sensors, highlighting discrete steps versus smooth, high-speed precision in robotics and automation.

Explore how feedback devices empower robots with real-time data on position, speed, force, and environment to achieve precision, stability, and adaptability in manipulation tasks.

Explore end effectors for robotic arms, including grippers, tools, sensor-based and vision-based systems, hybrid end effectors, and bioinspired options like octopus-inspired soft grippers.

Explore mechanical, vacuum, magnetic, adhesive, pneumatic, hydraulic, soft, and adaptive grippers, detailing their grasp functions and applications in assembly, material handling, delicate items, and high-speed tasks.

Explore online versus offline robot programming, including teach pendant, lead-through, and playback methods, and offline simulation with text-based coding for domains like welding, polishing, and automation.

Learn why matrix and homogeneous transformations are essential in robotic manipulators, linking forward kinematics to end-effector position and orientation via transformation matrices across revolute joints.

Explore Euler angles phi, theta, and psi that define a rigid body's orientation through three consecutive rotations about the x, y, and z axes - roll, pitch, and yaw.

Explore intrinsic and extrinsic Euler angle rotation sequences, where rotations about the body axis vs fixed world axes follow x y z conventions, with roll phi, pitch theta, and psi.

Compare extrinsic and intrinsic Euler angles, illustrating fixed-axis rotations (phi about x, theta about y, psi about z) versus rotating-axis conventions like zxz in robotics.

Derive the final rotation matrix for xyz intrinsic Euler angles by multiplying Rx(phi), Ry(theta), and Rz(psi), illustrating axis-specific rotations and the pitch, yaw convention.

Explain how Euler angles describe the end effector orientation and enable inverse kinematics and trajectory planning through orientation interpolation, while noting gimbal lock and Denavit-Hartenberg integration.

Explain how gimbal lock creates singularities in Euler angles when two axes align, reducing a manipulator's degrees of freedom, and discuss alternatives like quaternions or rotation-sequence changes to avoid it.

Explore homogeneous transformation, a 4 by 4 matrix that combines rotation and translation to determine the end effector's position and orientation relative to the base, using direction cosines.

Learn to compute end-effector position and orientation in robotic manipulators using 4x4 homogeneous transformation matrices. Analyze prismatic and revolute joints with translation and rotation about x, y, and z.

Explore why DH parameters matter for spatial linkages and robotic arms, enabling the end effector’s position and orientation from base using classical and modified conventions with four per joint.

Apply classical four-parameter method to compute forward kinematics by chaining transformation matrices from base to end effector, using theta, d, a, alpha and revolute joints.

Learn how to transform from frame i-1 to frame i using the Denavit-Hartenberg parameters, linking theta, d, a, and alpha to compute the end-effector pose.

Explore the modified dh parameters from frame i-1 to i, including alpha i-1, a i-1, theta i, and d i, and the sequence of operations to derive the transformation.

Apply the modified denavit-hartenberg transformation from frame i-1 to i using rotation about x, translation along x, rotation about z, and translation along z to build a 4x4 homogeneous matrix.

Compare classical and modified Denavit–Hartenberg parameters, detailing frame placement, axis directions, and the four DH parameters in each convention. Note both yield the same end-effector position, but orientation may differ.

Apply the right-hand rule to locate x, y, z axes for revolute and prismatic joints. Rotate about the z axis; positive rotation is counterclockwise seen from the top.

Frames describe how joints move one link relative to another, and DH convention uses frames and DH parameters to locate the end-effector for a six-dof manipulator with revolute and prismatic joints.

Explore frame assignment for a six-degree-of-freedom planar manipulator using the modified DH convention, detailing frames at proximal ends, twists, and DD parameters for revolute and prismatic joints.

Explains frame assignment and classical dh parameter calculation for a five dof 2d serial manipulator, detailing base and end-effector frames and dh parameters a, d, alpha, theta.

Explore classical dh parameters for a scara manipulator with four joints and learn to assign frames and compute the end-effector pose from base using transformation matrices.

Set all joints to zero to define the home position for the scara rrpr manipulator, yielding a transformation with x4 parallel to x0, y4 opposite y0, and z4 opposite z0.

Master the algorithm for frame assignment and modified dh parameters. Compare modified and classical conventions and apply the step-by-step process from base to end effector.

Explain the modified dh parameters for a scara rrpr manipulator, show frame assignments and how to derive transformation matrices to locate the end effector with respect to the base.

Analyze the home position of a scara (rrpr) manipulator using the modified dh convention, deriving the end-effector position from base to frame five and verifying the home transformation matrix.

Explore modified dh parameters for a spherical rrp manipulator, including frame assignments, twists, and the four parameters alpha, a, theta, and d. Derive the end-effector transformation relative to base.

Compute the home position of a spherical manipulator by setting theta1, theta2, theta3 to neutral values, deriving the frame zero to frame three transformation matrix, and confirming end effector orientation.

Apply modified DH parameters to a three-revolute articulated manipulator, define frames, compute twists and link offsets, and derive sequential transformation matrices to locate the end effector from base.

explains the home position of a three-revolute articulated manipulator using the modified DH convention, deriving the base-to-end-effector transformation with zero joint angles and offsets L2 and d1.

Explore how to apply modified DH parameters to a cylindrical manipulator with one revolute and two prismatic joints, assign frames, and derive the transformation matrices from base to end effector.

Determine the home position of the cylindrical manipulator using the modified dh convention by setting theta1 to zero and deriving the end effector location at x0, y d3, z d2.

Explore modified DH parameters for a Cartesian manipulator with three perpendicular prismatic joints, assign frames, and derive the transformation matrices to obtain the frame three with respect to the base.

Set theta1, theta2, theta3 to 90 degrees to define home position for a Cartesian manipulator; x3 aligns with x0, y3 opposite y0, z3 opposite z0, with position (d2, d1, -d3).