International Journal of Advanced Robotics
and Automation

The Automated Fiber Placement (AFP) machines have brought significant improvement on composite manufacturing. However, the current 7 DOF AFP machines normally consist of a 6 Degree-of-Freedom (DOF) serial robot and 1 DOF rotatory mandrel are designed for the manufacture of airframe components, which are usually shallow shells or tubes. They are not capable of handling some applications with more complex shapes. This paper presents the design and analysis of a 13 DOF collaborative AFP machine which consists of a 6 DOF manipulator, a 6-RSS (Revolute Spherical Spherical ) parallel robot and a spindle holding the mandrel (1 DOF) mounted on the platform of parallel robot. The collaborative machine modeling is carried out and the motion of the designed system is simulated in SimMechanics/ Matlab. The inverse kinematic models for both parallel and serial manipulators are established for path planning. In addition, the workspaces and singularities analysis of the collaborative AFP machine are carried out. The case study on three typical structures is presented and the simulation example for manufacturing of a hemisphere structure is provided. The simulation results show that the collaborative AFP machine could enlarge the manufacturing workspace, simplify the trajectory planning and enhance the production efficiency compared with the current 7 DOF AFP machine.

Keywords: Collaborative AFP, Parallel robot, Modeling, SimMechanics / Solidworks, Workspace, Kinematics

Composite materials are being widely used in many areas such as aerospace, automobiles, wind turbines, civil infrastructures [1]. These materials are generally lightweight and offer attractive strength-to-weight and stiffness-to-weight ratios over the traditional structural materials, such as steel, aluminum [2]. However, the traditional methods of producing composite components involve manual lay-up and tape-laying. These processes are time-consuming, labor intensive and hazardous, with high-material scrap rate and low repeatability [3,4].

The AFP machines have brought significant improvement on the manufacture of composite in terms of speed of material deposition, repeatability, good compaction, and reduction of waste [5]. But most AFP machines are designed for the manufacture of airframe components, which are usually shallow shells or tubes, and are not capable of handling some applications with more complex shapes. To be able to expand the manufacture capabilities of AFP machines in a simple and low cost way, it is necessary to increase the number of degrees of freedom of the robotic system.

One way is using another manipulator to hold the mandrel to be manufactured. The advantages of the integrated AFP manufacturing work cell using two serial manipulators are the large workspace and the dexterity to lay the fiber to manufacture the more complex geometry like human arms. But the load carrying capacity and the precision positioning capability are rather poor due to the cantilever structure of the serial manipulator [6]. For the applications of AFP machine where high load carrying capacity and precise positioning are of paramount importance, an alternative to such serial manipulators manufacturing work cell is desirable.

With the better stiffness and precise positioning capability [7], a 6 degree-of-freedom (DOF) parallel robot is introduced to AFP machines and a spindle is mounted on the platform to hold the mandrel [8]. The collaborative AFP manufacturing workcell is expected to be able to manufacture more intricate components and improve the product rate of the manufacturing compared with the current AFP machine. To our best knowledge, there is no application using the collaborative system (constructed with one parallel robot, one serial robot and one rotary stage) for AFP. And the most of the reported collaborative robotic systems usually consist of two serial robots used in other machining applications. The research on the design and analysis of the collaborative robotic system consisting of two different robots for AFP is very rare. In this paper, a 13 DOF collaborative AFP machine is designed by replacing the current 1 DOF mandrel holder with a 6-RSS (Revolutespherical- spherical) parallel robot and collaborating with a 6DOF serial robot. This paper aims at investigating the feasibility of applying such collaborative machine for fiber placement manufacturing. Hence the research topics include kinematic modeling, workspace analyzing and path planning of this 13 DOF machine.

For the serial manipulator, the forward and inverse kinematics is well-established. However, for the 6-RSS parallel manipulator, the forward kinematics poses a challenge due to the unique structure of fully parallel and closed-kinematic chains. Moreover, there might be multiple solutions to the forward kinematic equations [10- 12]. In this paper, the kinematic modeling of the designed system is carried out and the motion of the system is simulated in SimMecanics/Matlab. The inverse kinematic models of both serial and parallel manipulators are built for the path planning of fiber placement.

Finding the workspace free from singularities is very important for operating the collaborative AFP machine. One of the major disadvantages of parallel robot is the very limited and complicated workspace which is a highly coupled entity. Hence, for the parallel robots with more than three degree-of-freedoms, there will be no possible graphical illustration of the robot workspace. In the academic community, different types of subsets of the complete workspace are usually determined and the most popular one is the constant-orientation workspace which is the three–dimensional volume that can be attained by a point of the mobile platform while the platform is kept at a constant orientation [14-16]. Therefore, in order to get a good understanding of the parallel robot’s complete workspace, a series of constant-orientation workspaces for various orientations have to be studied. As the numerical methods, depending on the discretization step, give only an approximation of the shape of the workspace [17], the geometrical approaches are apparently faster, more intuitive, and accurate to analyze the workspace of parallel robots. The constant orientation workspace can be obtained by the intersection of six so-called vertex spaces and easily programmed in computer-aided design software such as Solid works [18-20]. In this paper, a geometrical method is used to analyze the workspace of the collaborative AFP machine and the singularity constraint condition is given for the parallel robot.

The path planning for the two 6DOF robots is a key technique for the fibre placement. In this paper, the manufacturing process is decomposed across the two robots involved [25]. The path planning decomposition follows the basic principle, i.e. to keep the fiber placement tip perpendicular to the surface mandrel without causing any collision and singularities while the motions of both robots are kept as simple as possible. To validate the developed modeling, workspace analysis and the path planning, a case study on three typical structures has been carried out and a simulation example for a bowl sample manufacturing is given to illustrate the mechanism of the designed collaborative AFP machine. The simulation results show that designed collaborative AFP machine could be able to enlarge the workspace to produce larger shape and simplify the path planning compared with the current AFP machine. Also, the designed machine can make the fiber placement process more flexible and can enhance the production efficiency.

The paper is organized as follows. In Section 2, the collaborative model is built and simulated in SimMechanics/Matlab and the inverse kinematic models are established for trajectory planning. The analysis of workspace and singularities of parallel platform is given in Section 3. In Section 4, path planning decomposition for collaborative AFP machine is introduced. In Section 5, three study cases are presented and a simulation example of hemisphere (bowl) manufacturing is provided. Finally, the simulation results validate the effectiveness of the proposed collaborative AFP manufacturing machine.

The experimental setup of the collaborative AFP machine consists of one 6 DOF serial manipulator, one 6 degree-of-freedom parallel robot and a spindle is mounted on the platform, as shown in Figure 1. The serial manipulator is Denso 6-Axis robot, model VP6242G, supplied with Quanser open-architecture control module which has all capabilities of an industrial system and is interfaced to QUARC. The fiber processing head will be attached to the robot’s end-effector. The 6-RSS parallel robot we used is Electric Motion System, model 710LP- 6-500-220, provided by Servo & Simulation Inc., which contains six identical kinematic chains connecting the base and the moving platform. Each connecting chain is composed of one horizontal revolute joint mounted on the base and two spherical joints. The motors and encoders

are located at the revolute joints on the base. The one degree-of-freedom spindle consists of one rotary stage and one three-jaw chuck. The rotary stage we used is AGR75-NC-9DU-BMS-R-3 with soloist CP controller from Aerotech Inc., which is mounted on the upper platform of the parallel robot. The three-jaw chuck is attached to the rotary stage to hold the mandrel. The pose of the mandrel can be controlled by the parallel robot.

The working principle of the collaborative AFP machine mimics the process of two hands lay-up. The serial robot holding the fiber process head is served as one hand. Through this hand, the tows fed from the fiber processing head are laid onto the mandrel. The parallel manipulator holding the mandrel by the three-jaw chuck is served as the other hand. The rotary axis of three-jaw chuck is perpendicular to the upper platform of parallel robot. The pose of the mandrel can be adjusted by the parallel robot. During the fiber placement process, the end-effector of serial robot must be orientated in such a way that the pressure of fiber processing head’s compaction roller always be normal to the surface of mandrel.

The main objective of this paper is to investigate the feasibility of applying the designed collaborative AFP machine to structure manufacturing. To achieve this objective, we use Matlab/SimMechanics to build the kinematic model for validating the subsequent workspace analysis and path planning. SimMechanics software is a block diagram modeling environment for the engineering design and simulation of rigid body machines and their motions, which interfaces seamlessly with Simulink and MATLAB. The visualization tools of SimMechanics software display and animate simplified standard geometries of 3 dimension machines, before and during simulation. Figure 2 shows the SimMechanics model of the collaborative AFP machine. The top part is the SimMechanics model of Stewart platform. The six identical kinematic chains connect the base and the moving platform. In each connecting chain, the proximal link is connected to the base by a revolute joint. The ends of the distal link are connected the proximal link and the moving platform by two spherical joints. Six drive signals are input to the actuator port of the six revolute joints. In addition, a spindle is mounted on the platform, connected by a revolute joint, to hold the mandrel. The bottom part of the figure shows the SimMechanics model of Denso Robot. Six revolute joints containing drive signals connect seven components including the end effector. The bases of the Stewart platform model and Denso Robot model are welded together. The positions and orientations of the two end effectors of the Stewart platform and the manipulator are measured by the sensors and output for further simulation.

Inverse Kinematic of Serial Robot: The serial robot model is built based on Denso Robot. The (D-H) Denavit–Hartenberg parameters, which represent the four parameters associated with a particular convention for attaching reference frames to the links of robot manipulator, are shown in Table 1.

There are multiple solutions to the inverse kinematics of a serial-link manipulator. The shortest distance rule is used to choose a solution closest to the current manipulator [9], shown in Equation (1).

where θ_i is the rotational angle of the i joint, θ_ni is the n solution.

The inverse kinematics of parallel robot is commonly used for trajectory generation. As described above, the inverse kinematics of the 6-RSS parallel robot is the mapping from the position and orientation of the end effect to the actuator angles, referring to the mechanism shown in Figure 3.

The end of each proximal link in the identical kinematic chain is connected to one of the six vertices of the base, point A_i . The coordinates of these points A_i (X_Ai Y_Ai Z_Ai) in terms of the base frameOare fixed and the values are shown in Equation 2.

where b and d are the side lengths of the base semiregular hexagon. The vectors along line OA_i are denoted as a_i.

The lengths of all proximal links are equal and denoted by r and the vector is defined as $$r=r{\left[\begin{array}{ccc}\cos {\theta }_i& 0& \sin {\theta }_i\end{array}\right]}^T$$ The connected points of the distal links and the proximal links are referred to as B_i . The horizontal rotational angles θ_i are controlled by the motors at revolute joints. The vectors along line OB_i in terms of the base frameO are denoted by b_i , shown in Equation 3.

Then the top ends of the distal links in the connecting chains are connected to the six vertices of the mobile platform, which are denoted as point T_i . The coordinates of these points T_i ( X_Ti,Y_Ti ,Z_Ti ) with respect to the upper frameO' are fixed, shown in Equation (4).

Where a and c are the side lengths of the top semiregular hexagon. The vectors along line O'T_i are denoted as t_i with respect to the upper platform. These coordinates vary in terms of the base frame when the platform moves. The position of the upper platform with respect to the base frame is defined by vector c , along the line OO' . The vectors along lines OT_i are denoted by d_i = c + Rt_i, which are the coordinates of all vertices of the upper platform with reference to the base frame (X_Ti Y_Ti ZT_i) . The transformation matrix R , defined by three Euler angles, describes the orientation of the upper platform. The unit vector along distal links L are denoted by n_i , which is

And

From the vector r and the vertices coordinates of points A_i and T_i with reference to the base frame, Eq. (7) reduces to

And

where $x_i=X_{T_i}-X_{A_i}{z}_i=Z_{T_i}-Z_{A_i}$ and $p_i=\frac{{\Vert d_i-a_i\Vert }^2+r^2-L^2}{2r}$ The inequality $x_i^2+z_i^2-p_i^2\ge 0$ holds.And ${\theta }_i\in \left[-\pi ,\pi \right]$ is the solution to the inverse kinematics

In this paper, the three–dimensional workspace can be attained by keeping a center point o' (x, y, z) of the mobile platform at a constant orientation. In order to get the position points of o', the transformation matrix ${}_p{}^{b}T$defined as ${}_p{}^{b}T=\left[\begin{array}{cccc}\ddots & & & x\\ & R& & y\\ & & \ddots & z\\ 0& 0& 0& 1\end{array}\right]$ , and the position of points $T_i$ in terms of the base frame O is obtained as
$\left[\begin{array}{c}{X}_{T_{\text{i}}}\\ Y_{T_{\text{i}}}\\ Z_{T_{\text{i}}}\\ 1\end{array}\right]=\left[\begin{array}{cccc}\ddots & & & x\\ & R& & y\\ & & \ddots & z\\ 0& 0& 0& 1\end{array}\right]\left[\begin{array}{c}{x}_{T_{\text{i}}}\\ y_{T_{\text{i}}}\\ z_{T_{\text{i}}}\\ 1\end{array}\right]=\left[\begin{array}{c}M(1,1)+x\\ M(2,1)+y\\ M(3,1)+z\\ 1\end{array}\right]$ $${(x-x_i)}^2+{(y-y_i)}^2+{(z-z_i)}^2=L^2$$ $$x_1=X_{B_1}-M(1,1)+r\times \cos (pi/6+{\theta }_1)$$ $$y_1=Y_{B_1}-M(2,1)$$ $$z_1=Z_{B_1}-M(3,1)-r\cdot \sin (pi/6+{\theta }_1)$$ $$\begin{array}{l}r\cdot \cos (pi/6+{\theta }_1)=x_1-X_{B_1}+M(1,1)\\ r\cdot \sin (pi/6+{\theta }_1)=z_1-Z_{B_1}+M(3,1)\end{array}$$ $$as{\theta }_i\in \left[-\pi ,\pi \right].$$ $${(x_1-x_{o1})}^2+{(z_1-z_{o1})}^2=r^2$$ $$\begin{array}{l}{x}_{o1}=X_{B_1}-M(1,1)\\ z_{o1}=Z_{B_1}-M(3,1)\end{array}$$ $$L{n}_i{}^T\left(\dot{c}+\dot{R}{t}_i-r{\left[\begin{array}{ccc}-\sin {\theta }_i& 0& \cos {\theta }_i\end{array}\right]}^T{\dot{\theta }}_i\right)=0$$ $$L{n}_i=\left[\begin{array}{c}{X}_{T_i}-X_{A_i}-r\cos {\theta }_i\\ Y_{T_i}-Y_{A_i}\\ Z_{T_i}-Z_{A_i}-r\sin {\theta }_i\end{array}\right]$$ $$L\left[{\begin{array}{cc}{n}_i{}^T& \left(t_b{}_i\times n_i\right)\end{array}}^T\right]\left[\begin{array}{c}\dot{c}\\ \omega \end{array}\right]=r\left(z_i\cos {\theta }_i-x_i\sin {\theta }_i\right){\dot{\theta }}_i$$ $$L\left[\begin{array}{cc}{n}_1{}^T& {\left(t_b{}_1\times n_1\right)}^T\\ ⋮& ⋮\\ n_6{}^T& {\left(t_b{}_6\times n_6\right)}^T\end{array}\right]\upsilon =r\left[\begin{array}{ccc}\mp \sqrt{x_1^2+z_1^2-p_1^2}& & 0\\ & \ddots & \\ 0& & \mp \sqrt{x_6^2+z_6^2-p_6^2}\end{array}\right]\dot{\theta }$$ $$f\left(u,v\right)=ax\left(u,v\right)+by\left(u,v\right)+cz\left(u,v\right)+d=0$$ $$\begin{array}{l}{e}_1={\left[\begin{array}{ccc}{e}_{1x}& e_{1y}& e_{1z}\end{array}\right]}^T=\frac{c\text{'}(t)}{\left|c\text{'}(t)\right|}\\ e_2={\left[\begin{array}{ccc}{e}_{2x}& e_{2y}& e_{2z}\end{array}\right]}^T=\frac{n(t)}{\left|n(t)\right|}\\ e_3={\left[\begin{array}{ccc}{e}_{3x}& e_{3y}& e_{3z}\end{array}\right]}^T=e_2(t)\times e_1(t)\end{array}$$