**4. The weaknesses of the motion geometry for T-S Robot**

Although T-S Robot has so many advantages such as high precision, speed, stiffness, and lack of singularity in workspace, it has two main weaknesses:


Therefore, to remove the first problem, a robot with telescopic arms, **Figure 3** (**a**, **b**), is intro‐ duced whose kinematics are conducted without getting involved in the whole discussion.

To remove the second problem, new robots with improved structures are introduced. The schematic design of these robots, **Figure 4** (**a**, **b**) and their three-dimensional designs in the kinematics analysis section of each robot in **Figure 14a** and **Figure 14b** along with robot motion geometry structure are shown.

Kinematic Analysis of the Triangle-Star Robot with Telescopic Arm and Three Kinematics Chains as T-S Robot (3-PRP) http://dx.doi.org/10.5772/64556 71

1

= -- +å (1)

=

*N* = The number of arms, *L* = The number of robotic joints, *fi* = Indicated of DOF related *i* joint as shown in the above mentioned table. On the other hand, in the parallel manipulator robot,

for *i* = 1,…,9 equals 1, thus the robot's DOF is equal to 3.

**Joint Diagram Symbol DOF** Revolute R 1

Prismatic P 1

Cylindric C 2

Universal T 2

Spherical S 3

**4. The weaknesses of the motion geometry for T-S Robot**

of singularity in workspace, it has two main weaknesses:

**2.** The abovementioned robot has a rather limited workspace

Although T-S Robot has so many advantages such as high precision, speed, stiffness, and lack

Therefore, to remove the first problem, a robot with telescopic arms, **Figure 3** (**a**, **b**), is intro‐ duced whose kinematics are conducted without getting involved in the whole discussion.

To remove the second problem, new robots with improved structures are introduced. The schematic design of these robots, **Figure 4** (**a**, **b**) and their three-dimensional designs in the kinematics analysis section of each robot in **Figure 14a** and **Figure 14b** along with robot motion

**1.** At the time of Robotic motion, the star arms occupy a large space around the triangle

*n i i*

6 1

*N* = 8, *L* = 9 and *fi*

70 Recent Advances in Robotic Systems

**Table 1.** DOF for type of joint [9].

geometry structure are shown.

*F (N L ) f*

**Figure 3.** (a) Real model of the Triangle-Star Robot' components with telescopic arms. (b) The Triangle-Star Robot (T-S Robot) with telescopic arms. (c) The geometric model of T-S Robot with telescopic arms.

**Figure 4.** (a) Introduction a new geometric model as Reuleaux Triangle-Star Robot with telescopic arms. (b) Introduc‐ tion of a new geometric model as Circle-Star robot with telescopic arms.

These robots are as follows:

