There are five identifiable stages in the computer solution of a problem in computational science and engineering. In this article is using the modeling of a robotic arm to present the stages of computational science and engineering. The case study considers the kinematics of a robotic arm. We use this opportunity to discuss several ideas about programming in the C++ language. We will discuss how variables, data types, and assignments are expressed in C++. Each of these stages is presented as a separate section is this lesson.
The robotic arm contains of two limb sections, the arm and the forearm, connected at a joint, the elbow. The arm is attached at the other end to the body, and the forearm could be connected to a hand. The limbs are connected at their endpoints by joints, shoulder and elbow, that are allowed to rotate in a planar motion.
The problem is to determine the X-Y position of the robotic wrist joint given the angle arm makes with the body, the angle that the forearm makes with the arm, and the length of the limb segments.
The X-Y position of the shoulder joint is fixed. The top endpoint of the arm link is attached at the
shoulder joint. The arm can rotate around the shoulder joint. The arm must always be attached to the shoulder. The forearm link is connected to the arm link, and the hand link would be connected to the arm link.
We represent the movement of the robotic arm by the coordinates of the joints in the X-Y plane. The motion of the arm is determined by the angle, alpha, that the arm makes with the body, by the angle, beta, that the forearm makes with the arm, and by the lengths of the links. The lengths of the segments are shown in the link diagram.
The angle alpha will be measured in degrees counterclockwise from the positive Y axis. The angle beta will be measured in degrees clockwise from the arm to the forearm. When the arm is raised to the horizontal position, the angle alpha is degrees and the angle beta is 180 degrees.
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