Verification and Generation of Safe Straight Paths for a 4-DOF Spherical Manipulator

• Main Author: Rawand Ehsan J.T.
• Format: Article
• Language: English
• Published: Tikrit University 2013-04-01
• Series: Tikrit Journal of Engineering Sciences
• Subjects: Singularity, Jacobian matrix, rank deficiency, path generation, kinematics, configuration
• Online Access: http://www.tj-es.com/ojs/index.php/tjes/article/view/117
• ISSN: 1813-162X; 2312-7589

<p>Sometimes in a manufacturing environment, a robotic arm is wanted to move in a straight path such as welding, painting and assembling. This straight path causes the manipulator to actuate all or most of its joints in the same time to track the path. Along this path, the manipulator may reach a specific singular configuration in its workspace at which one or more joints are in their limits, or a part of the path lies outside the workspace. These conditions make the arm’s movement be unsmooth and may cause damage to the manufacturing process. In this paper, the singularities inside the workspace of a 4-DOF spherical manipulator are indicated and a method is presented for finding the arm configurations (assuming that all joints are actuated at the same time) along a straight path between an initial and a goal configurations. All joint limits are presented and if a part of the path lies outside the workspace, the model processes this condition by introducing a new initial configuration through changing the third joint’s (q₃) position only. A smooth straight path is generated between any two configurations using the parametric equations of the line connecting them. Unlike the analytical inverse kinematics, which needs a (4 x 4) homogeneous transformations convention matrix (DH) to find the joint variables, this method needs only the initial configuration, goal configuration, link lengths and the corresponding Cartesian coordinates of the path. It always gives the correct solution for the under taken path.</p><p><strong> </strong></p>