Robotics design and simulation part 1

Explain two-dimensional matrices defined by rows and columns, and perform addition, subtraction, and multiplication with compatible dimensions, while noting vectors, scalars, and MATLAB as next steps.

Explore matrix operations, including transpose, identity matrices, and column-to-row transformations. Apply these techniques to compute inverses with extended methods and solve linear systems using matrices.

Learn to compute and manipulate matrices in MATLAB by creating incremental matrices, indexing rows and columns, extracting submatrices with colon notation, and updating elements.

Learn how to create and use MATLAB functions, including single and multi-input/output forms, define with the function keyword, save scripts, and call them from the command window.

Open Simulink to start a new model and navigate the block library to build simple models using constant, product, and function blocks to simulate signals and explore MATLAB workspace variables.

Master vector addition and dot product in robotics, relate base and end-effector position vectors, and compute magnitudes, projections, and axis components using angle and cosine relationships.

This chapter introduces spatial descriptions of transformation, covering position, orientation, frames, and transformation matrices to move between points in space for robotic manipulators as open kinematic chains with six joints.

define coordinate systems, use vectors to describe position, and attach frames to each body to describe orientation in two-dimensional and three-dimensional space.

Analyze the rotation in the 2d plane between coordinate systems zero and one, by angle theta about the z axis. Use unit vectors and projections to derive the rotation relations.

describe spatial relations with frames and coordinate systems, represent positions by vectors, orientations by rotations, and apply transformations to convert coordinates between frames.

Learn how to use a 4x4 transformation matrix to combine rotation and translation between robot frames, and translate points across base and end-effector coordinates.

Explore how orientation can be described with three-parameter representations beyond rotation matrices, including fixed-axes xyz rotations and z-y-x Euler angles, and how rotation order and frame choice affect orientation.

Define kinematics and the kinematic chain, introduce a convention for forward and inverse kinematics, and distinguish Cartesian space from joint space with revolute and prismatic joints.

Introduce the Denavit-Hartenberg convention for robot kinematics, define the four joint parameters theta, d, a, alpha, and build and multiply homogeneous transformation matrices to relate link frames.

Explore six-DOF Puma robot kinematics through a practical example, assign frames and DH parameters, and implement transformation matrices in MATLAB to compare with SolidWorks.

Learn a six degrees of freedom puma robot example in matlab by constructing and multiplying six transformation matrices to obtain the end effector pose relative to the base.

Explore how to assign frames and compute DH parameters for the Stanford manipulator. Analyze revolute and prismatic joints and construct transformation matrices from base to end-effector.

Explore four-degree-of-freedom scara kinematics using matlab, building forward kinematics from transformation matrices with correct multiplication order, and validate results against solidworks visuals before moving to inverse kinematics.

Learn to derive explicit inverse kinematics from transformation matrices of a robot arm. Solve nonlinear equations for joint variables and navigate multiple solutions and workspace limits.

Solve inverse kinematics by decoupling position and orientation for a six-joint robot, locate the wrist center to determine the base position, and compute the end effector orientation via rotation matrices.

solve the inverse position problem with a geometric approach to find theta1, theta2, theta3 for a robotic manipulator, address plane projections, line of rejection, and singular configurations.

Explores solving the inverse orientation problem for a six-DOF robot wrist using Z-Y-Z Euler angles, deriving theta4–theta6 from the rotation matrix, and addressing singular configurations with multiple solutions.

Solve the inverse kinematics for the Puma robot by decoupling position and orientation, deriving joint variables from the end-effector transformation matrix and handling left and right arm configurations.

Solve the inverse position and orientation problems for a Stanford robot example by deriving joint variables from a transformation matrix, computing X, Y, Z, theta1, theta2, and Euler angles.