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The design, dynamics, and workspace of a hybrid-driven-based cable parallel manipulator (HDCPM) are presented. The HDCPM is able to perform high efficiency, heavy load, and high-performance motion due to the advantages of both the cable parallel manipulator and the hybrid-driven planar five-bar mechanism. The design is performed according to theories of mechanism structure synthesis for cable parallel manipulators. The dynamic formulation of the HDCPM is established on the basis of Newton-Euler method. The workspace of the manipulator is analyzed additionally. As an example, a completely restrained HDCPM with 3 degrees of freedom is studied in simulation in order to verify the validity of the proposed design, workspace, and dynamic analysis. The simulation results, compared with the theoretical analysis, and the case study previously performed show that the manipulator design is reasonable and the mathematical models are correct, which provides the theoretical basis for future physical prototype and control system design.

In manipulation systems, it is always a goal to continuously improve the range of motion, accuracy, and load capacities. Compared with the traditional mechanical structures, parallel mechanisms have the advantages of high dexterity and accuracy. Cable parallel manipulators (CPMs) are categorized as a type of parallel manipulators. They are a variant of the Gough-Stewart platform in which rigid extensible legs are replaced by cables stored spools. CPMs have several advantages over rigid-link mechanisms, such as (i) remote location of motors and controls, (ii) rapid deployability, (iii) potentially large workspaces and (iv) high load capacity; (v) reliability [

The first written information on use of hoist mechanism in ancient Greece appeared around 530 BC, which is concerned with the construction of the first temple of Artemis in Ephesus, and temples at Selinous, temples of Apollo at Syracuse and at Corinth. After 515 BC, cranes were in common use [

As we are aware, there are relatively fewer published works on the drive system of the CPMs, which is the main contribution of this work. The existing research on the drive system of the CPMs usually uses the low power controllable motor. In the recent years, as the CPMs have been investigated widely for various applications in modern manufacturing, they are required not only for operations with high accuracy and high payload, but also for output with greater flexibility, which can change the law of output motion quickly and conveniently [

The hybrid-driven planar five-bar mechanism (HDPM) is a kind of machine whose drive system consists of a constant velocity (CV) motor and a servomotor [

It is well known that dynamic performance has a great impact on the operation of the manipulator, and this is on the basis of its dynamic control. As demonstrated in [

The workspace is also one of the most useful measures for the evaluation of the manipulator performances [

In the rest of the paper, Section

In this paper, for the purpose of analytical modeling and numerical analysis, the three-dimensional design model of the completely restrained HDCPM with three translational motions is taken as an example (see Figure

Three-dimensional model of the HDCPM.

Mechanical configuration of the HDCPM: (a) front view, (b) top view.

The working process of the HDCPM is as follows. The CV three-phase asynchronous motors and servomotors are power sources. On the one hand, the servomotor and the reducer are linked by the coupling, then the servomotors through a small crank disk are connected with a short rod connection thus adjusting the output motion of the HDPM. On the other hand, each CV three-phase asynchronous motor is connected with the pulley transmission mechanisms, then it links to a long connecting rod by a large crank disk, thus providing the main power for the HDCPM. These two types of input motions are hinged through the short and long connecting rod, so that the power distribution and other characteristics of the HDPM are improved while ensuring the output motions. Four groups of the HDPM with the same structure produce rotary motion, thus the four cables can be driven in order to realize the output motion trajectory of the end-effector.

A simple schematic sketch of the HDCPM structure model with the associated coordinate systems is depicted in Figure

Structure model (a) of the HDPM and schematic sketch (b) of the HDCPM.

Link

In (

Let

The relationships between the cable length

Newton’s law for the end-effector of the HDCPM results in

Thus the dynamic model can be expressed as follows:

The dynamic model of the HDCPM is presented in two parts. The first is directed to the structural model (CPM) above, the other one to the actuator dynamics (servomechanism). Applying the Newton-Euler equation establishes the dynamic model of the HDPM. The force analysis of each link of the HDPM is shown in Figure

Free body diagrams of the HDPM: (a) link

By the force analysis mentioned previously, the Newton-Euler formulation of the links can be listed as follows.

Link

Link

Link

Link

The equation can be summarized as

Taking into account (

The workspace of the HDCPM is characterized as the set of points where the end-effector can be positioned while all cables are in tension (

The workspace of the HDPM. According to (

The motion range of the end-effector for the HDCPM can be written in the following form:

A general numerical workspace generation approach is employed here. The possible motion range of joint

From

Similarly,

Record

Various combinations of

and those satisfying motion range of the end-effector

and tension condition

Simulation studies were performed with the software named MATLAB 2010. A three-dimensional simulation model of the HDCPM has been established, where the four groups of HDPMs have the same structure parameters and symmetry in the three-dimensional space. The parameters of the HDCPM are listed in Table

Parameters of the HDCPM.

System parameters | Value |
---|---|

Mass of the end-effector |
20 kg |

Acceleration due to gravity |
9.81 m/s^{2} |

Height of the cable tower rack |
1 m |

Side length of four towers distributed in rectangle |
1 m |

Side length of four towers distributed in rectangle |
1 m |

Length of the cable |
2.3 m |

Length of the |
1 m |

Length of the Link |
0.2 m |

Length of the Link |
0.5 m |

Length of the Link |
0.5 m |

Length of the Link |
0.28 m |

Length of the Link |
0.51 m |

Density of the Links |
^{3} |

Cross-sectional area of the Links |
^{2} |

This section presents two motion cases of the end-effector for dynamic simulation.

The equation of the circle with a radius of 0.25 m parallel to the

Following trajectory of the circle motion.

Figure

Time behavior of cable length for Case

Curves of cable tension for Case

The kinematic parameters of the HDPM can be obtained by the inverse kinematics of the HDCPM, for given end-effector position. The angle of joint

From (

According to (

Solving (

According to the inverse kinematics analysis of the HDCPM above, one can calculate the angular variables for all links of the HDPM as the end-effector moves along the circle. Figure

Curves of the links motion parameters of the HDPM for Case

Trajectory of joint

Figure

Resultant force curves of the joints of the HDPM for Case

If the cables are driven only by coils and servomotors, which is a classical approach for the conventional CPM, the range and speed of obtainable output motions may be limited by certain servomotor power capacity and high cost. This problem can be solved by using hybrid-driven machines instead of coils and servomotors. For the hybrid-driven machines, the CV motor provides the majority of power supply to drive the mechanism’s motion. The servomotor is real-time controllable and offline programmable [

The CV motor power and servomotor power of the HDPM can be calculated by

Figure

Motor absolute value power curves of the four groups of HDPMs of the HDCPM.

As the motion circular trajectory of the end-effector is the same, and as the structural parameters of the classical approach for the conventional CPM are the same (cables are driven only by coils and servomotors), the servomotor power of the conventional CPM can be obtained by

Figure

Servomotor absolute value power curves of the conventional CPM.

Comparison of absolute value power curves between the HDCPM and conventional CPM.

In order to investigate the power property of the HDCPM further, the following simulation is performed as the CV motors of the four groups of the HDPMs of the HDCPM run with 1.1 rad/s (

Curves of the links motion parameters of the HDPM as

Motor absolute value power curves of the four groups of HDPMs of the HDCPM as

Comparison of absolute value power curves between the HDCPM as

The equation of the line in global coordinate system is

Figure

Figure

The angular variables of links of the HDPM for Case

The resulting force curves of the joints of the HDPM for Case

From the results and discussions, illustrative simulation studies highlight its performances, which lay a foundation for the further research on optimization and real-time control.

Following trajectory of the line segment motion.

Curves of cable length for Case

Curves of cable tension for Case

Curves of the links motion parameters of the HDPM for Case

Running trajectory of the joint

Resultant force curves of the joints of the HDPM for Case

Comparison of absolute value power curves between the HDCPM and conventional CPM for Case

The workspace of joint

Workspace of joint

Workspace of the HDCPM (a) and projections of workspace onto

This paper describes the theoretical investigations of a class of the completely restrained hybrid-driven based cable parallel manipulators (HDCPMs) with three translational motions. The HDCPM combines the advantages of four groups of HDPMs and a 4-cable parallel manipulator in a way to provide a solution for moving heavy objects with high efficiency and high performance. Detailed design and implementation of a virtual prototype model of the HDCPM is presented as well. Dynamic modeling of the full system including both the mechanical system and the driving system is addressed. The inverse kinematic and dynamic problems of the HDCPM system are resolved on condition that an operation path of the end-effector has been planned. Then, the main factors, which influence the workspace of the HDCPM such as workspace of the HDPM and the length of cables, are analyzed based on the structure constraints of the HDCPM. Finally, illustrative examples for trajectory tracking and workspace demonstrate that the manipulator design is reasonable and the associated models are correct.

The prototype verification of the designed HDCPM is currently under investigation. Furthermore, more work is in progress to implement control system design, design modification, and optimum synthesis for the HDCPM. In addition, the methodology presented in this work could be used as a guide for the design and analysis of other manipulators.

This work was supported by the National Natural Science Foundation of China (50905179, 51275515), Program for Innovative Research Team in University (IRT1292), the Six Talent Peak Foundation of Jiangsu Province, and the Priority Academic Programme Development of Jiangsu Higher Education Institutions. The authors also appreciate the comments and valuable suggestions of anonymous referees and editors to improve the quality of the paper.