Application of Forward Kinematic Methods and Jacobi Matrix in Analyzing The Singular Conditions of The Kawasaki Industrial Series Robots

Abstract

In designing a manipulator, several things need to be considered, which is like the singular condition of the manipulator. This is so that the manipulators can operate in a safe work area. This research will begin with modeling 3D serial manipulator 6R using Inventor software. This 3D model is needed to get join parameter  values, namely a, d, θ and α. After obtaining the join parameters, a Forward Kinematic calculation is performed to get the end effector position when given a certain input angle using Matlab software. Then variations are made on the input angle θ2 (30° to 180°) and θ3 (-90° to 60°) and a graph that shows working spaceis obtained. To ensure that the calculations performed are correct, validation using inventor is done by providing an angle value for the second and third joints. Then the Jacobian matrix was built to obtain the singularity value of each configuration by determining the Jacobian matrix. The configuration is stated to be in a singular position if the det (J) is approaches 0. With the variation in input angle obtained, the manipulator range is  -471 mm to 2967 mm on the Z axis and -1936 mm to 2699 mm on the X axis. The singular manipulator is occur when θ3 = -78.15 ̊. From these results it can be stated that the manipulator cannot be in the configuration of θ3 = -78.15 ̊. This is in line with the manufacturer's recommendations which only allow θ3 minimum is -75 ̊..