Inverse Kinematics Analysis of 5-DOF Robot Manipulators Based on Virtual Joint Method

Abstract

To solve the inverse kinematics problem of a robot manipulator without closed form solutions, one-dimensional iterative method is very useful. However, for a 5-DOF robot manipulator, because of the uncontrolable and uncertain orientation vectors, it's difficult to analytically express all joint variables by one of them, therefore one-dimensional iterative method can not be directedly used. By adding an appropriate virtual joint to it, a 5-DOF manipulator can be changed into a 6-DOF one so that the uncertain orientation vectors can be pre-given, and the difficulty is solved. To illustrate this virtual joint method a 5-DOF serial robot manipulator with prismatic arm joint and offset wrist is discussed in this paper as an example.

5-DOF serial robot manipulator design, application and inverse kinematic solution through analytical method and simple search technique

“…Where, −1 , s and c are transformation matrix between two consecutive coordinate systems, sine and cosine, respectively (i=1,2,⋯, 9). And, the obtained transformation matrices are as follows; The forward kinematic equations of the mechanism can be obtained by multiplying these transformation matrices and consequently, the transformation matrix which defines the position and orientation of the end effector according to the base coordinate system can be written as in Eq.…”

“…In this technique, the authors randomly selected the first joint variable of the sample mechanism and then calculated the other joint variables iteratively, depending on this value. Liu et al [9] solved the inverse kinematic problem of a five DOF serial robot manipulator through a method called virtual joint approach. Sarıyıldız and his colleagues [10] compared three different screw theory-based methods in order to solve the inverse kinematic problem of serial industrial robot manipulators.…”

Flexible sensing-based knee joint flexion monitoring system

“…Compared with traditional large medical instruments, wearable devices are favored due to their portability, which not only solve the problems such as the postoperative rehabilitation effect of TKA is not easy to quantify, but also reduces the cost of rehabilitation [8] . There have been many applications of wearable devices in knee rehabilitation assessment, Majumder used a wearable-based low-power IMU to achieve the tracking and monitoring of lower limb joint angles, and achieved real-time estimation of lower limb joint angles by a two-stage fusion algorithm [9] ; Liu K proposed a wearable sensor construction method based on accelerometer and magnetometer with a non-invasive virtual sensor to detect assessment of three-dimensional kinematic parameters of lower limb joints, which can be applied to gait analysis [10] . Although these wearable devices can effectively assess the status of the patient's knee joint for rehabilitation outcome assessment, wearing these rigid devices made of silicon-based is prone to cause injury to the patient's soon-healed joint.…”

Inverse Kinematics and Model Calibration Optimization of a Five-D.O.F. Robot for Repairing the Surface Profiles of Hydraulic Turbine Blades

“…An iterative approach can be found in [15] for solving inverse kinematics by adding a virtual joint to the five-d.o.f. robot, expressing all joints by one variable and applying the one-dimensional iterative Newton-Raphson method to minimize the tip-position error.…”