**2. Geometric characteristics of the Triangle-Star Robot**

The geometric model of the Triangle-Star Robot (T-S Robot), shown in **Figure 1** (**a**, **b**), is composed of a *A*<sup>1</sup> *A*<sup>2</sup> *A*<sup>3</sup> fixed triangle and a moving star with *B*<sup>1</sup> *B*<sup>2</sup> *B*<sup>3</sup> arms in which the *B* star can move on triangle *A* with three kinematics chains 3-PRP.

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 69

**Figure 1.** (a) The Triangle-Star Robot (T-S Robot) with rigid arms and (b) the geometric model of T-S Robot with rigid arms.

The motion geometry of each of the kinematics chains 3-PRP, which has been applied to T-S Robot, is achieved through relative movement of the Prismatic joint, Revolute joint, and again the Prismatic joint as shown in **Figure 2**.

**Figure 2.** The motion geometry of the kinematics chains (3-PRP) for T-S Robot.

move toward a practical system to produce the maximum production variety at minimum time with the lowest expenses and the highest quality. Thus, the industrial automation with the help

Today, robots are divided into several groups: Serial robots, Parallel robots, Synthetic robots, and Mobile robots [2, 5]. Synthetic robots are to incorporate the serial and parallel manipulators by connecting them in serial. The serial connections of serial and parallel manipulators can be categorized into the following four types: Parallel-Parallel, Serial-Parallel, Parallel-Serial, and Serial-Serial [8]. Characteristics such as precision, speed, stiffness, and a workspace without singularity points have differentiated the Parallel robot from the Serial robots [4, 5]. The Parallel manipulator robots are used in making flight simulators, helicopters, machinery tools, precise robots, etc. The reverse kinematics solution of these robots as compared with the simple Serial robots and direct kinematics solution is hard with complicated equations [3, 8]. In this paper, first, the geometric attributes of the Triangle-Star Robot are offered and then based on motion geometry and robotic workspace, the limitations and weaknesses are recognized and indexically represented. In addition, to removing the abovementioned shortcomings, a new Triangle-Star Robot with telescopic arms and two new robots with improved structures are represented. Finally, the kinematics analysis of the robots similar to Denavit–Hartenberg

The geometric model of the Triangle-Star Robot (T-S Robot), shown in **Figure 1** (**a**, **b**), is composed of a *A*<sup>1</sup> *A*<sup>2</sup> *A*<sup>3</sup> fixed triangle and a moving star with *B*<sup>1</sup> *B*<sup>2</sup> *B*<sup>3</sup> arms in which the *B* star

of robots replaces human force in production and in assembly lines.

**2. Geometric characteristics of the Triangle-Star Robot**

can move on triangle *A* with three kinematics chains 3-PRP.

(a)

approach is carried out.

68 Recent Advances in Robotic Systems

The lower active Prismatic joint movement joined to the stimulator in the direction of the angle of the triangle causes movement in the upper passive Prismatic joint connected to lower active Prismatic joint by the Revolute joint. As a result, star motion geometry, which is sited (fixed) on the upper Prismatic joints, serves as a function of the lower Prismatic movement joined to the stimulators.
