Consider a planar parallel robot used in a surgical procedure to position a needle above the patient, see

Figure $1.$

Figure $1.$ Needle positioning Parallel Robot.

The parallel robot consists of a fixed Base Plate, a Moving Platform, six passive revolute joints and

$P{P}_i$ where $\{$:$i=1$:$3)$ and three active revolute joints where $\{$:$i=1$:$3).$ The $i^{th}$ strut of the robot consists

therefore of three joints that are subdivided in the upper section $s_A,$ and the lower section $L.$ For

further information to the robot see its kinematic model in Figure $2.$

Develop a kinematic simulation of the parallel robot in MATLAB to:

Solve and implement parallel robot Inverse Kinematics. Calculate the joint coordinates ${}_i$ where

$i=1$:$3$ from the Cartesian parameters of the Platform's centre $\{C\}($where the needle is based$).$

These parameters are the $(x_c,Y_c)$ coordinates and the orientation of the platform $($a$).$ Plot the

kinematic model in two different positions. Changing the Cartesian input parameters should

adapt each leg to the new Cartesian position. An example plot is shown in Figure $3.$

Plot the Parallel robots workspace for a given orientation $a.$ This is crucial for the mechanism

synthesis analysis.