七自由度机械臂运动学仿真（Inverse Kinematics Simulation）
1. Objective
Inverse Kinematics is used to get the Joint angles based on the Cartesian space position.
In some situations, RCM part need to achieve some positions then mapping to the Master Hand, there is also a desired position. Then we need to know how to adjust the joint to achieve it.
2. Method
（1）Using Robotics Toolbox
For the example, the initial point is the initial configuration and the target point is T2.
T1 = transl(0.35,0,-0.1653) * troty(-pi/2);
T2 = transl(0.2,0.1,0) * trotx(pi/2);
Fig shows the Master Hand in the initial configuration.
Fig shows the angles of each joint with respect to time.
The animation based on given trajectory.
（2）Using Robotics System Toolbox
For the example, the way points are selected as followed.
wayPoints = [0.2 -0.2 0.02;0.25 0 0.15; 0.2 0.2 0.02]
Fig shows the Master Hand in the initial configuration.
Fig shows the desired trajectory of end-effector
The animation based on given trajectory
（3）Using Inverse Kinematics Algorithm
For the example, the trajectory is given as followed.
xd = [0.25*(1-cos(pi*t));0.25*(1-sin(pi*t)); 0*t];
xd_dot = [0.25*pi*sin(pi*t);-0.25*pi*cos(pi*t); 0*t];
Fig shows the trajectory of end-effector
The circle trajectory in 3D model
3. Simulation
After calculate the joint angles, we can input to simmechanics model and see the simulation in the real model. Using the function of simmechanics, it is easy to sense the joint status including position, velocity, acceleration, torque or force.
Animation of first two ik method
You can easily sense the data from simscape model, such as position of end-effector.
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