Inverse Kinematics on MENTOR Arm

In this article we will talk about using inverse kinematics on the Mentor arm. The purpose of this is to position the wrist position of the Mentor Arm according to the x,y,z coordinates that we get from leap motion (will be discussed in a future post). 

Figure 1: Overview of Palm position and the wrist position

What is Inverse Kinematics? This method computes all possible sets of joint angles and link geometries which could be used to attain the given position and orientation of the end effector [1].  

As mentioned in the previous post Mentor Arm has 6 degrees of freedom. However in this project we are using IK only for 2dof (on x and y plane). The simplified version has only two joints where as shown in figure 2, they are Top arm joint 3 and Bot arm joint 2. 

Figure 2

To start this the simple two link manipulator is shown below, 

Figure 3

Using trigonometry,

These equations can be used to find the position of each bar in terms of angles. So the manipulator links can move to the specific location according to the calculated angles.

In general these IK equations does not give an unique solution. The above inverse cosine can give two solutions either positive or negative. 

Figure 4

[1] Wilson and Sadler: Kinematics and Dynamics of Machinery: Chapter 12