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MENG 356- Mechanical Design I

Term Project
Six DOF Hexapod
Challenge of Design and Innovation

Presented to:
Dr. Hani Ali Arafa

Presented by:
Moataz Mohammad Attallah
Ola Rashwan


  I -  Abstract

  II -  History:
 ·  Manipulators and Hexapods
 ·  Stewart Platform: first generation of 6 DOF devices
 ·  Early applications
 ·  Limitations and shortcomings of the early hexapods
 ·  Conclusion

  III -  Description of the Hexapod:
 ·  Different designs
 ·  Kinematics: Degrees of freedom analysis (Over constraints/Local mobility)
 ·  Current research and modifications into the design.

  IV -  Applications:
 ·  Flight and motion simulators
 ·  Manufacturing Technology
 ·  Precision positioning in medical applications
 ·  Other applications and current research

V- Conclusion:
 ·  Advantages over other similar devices
 ·  Disadvantages
 ·  Future developments and current research

  VI -  Bibliography

  VII -  Appendix


The aim of this term project is to introduce a new family of positional devices, called Hexapods. This relatively new joint is an example for parallel manipulators. The idea of the design was based on a design introduced by D. Stewart for a manipulator that he termed Stewart Platform. The report introduces the conventional Stewart platform and other new designs that are based on the same idea, in addition to calculation of the DOF for these designs. The report also highlights current and future applications for the hexapod. In addition, it traces the limitations and advantages of the new designs over the old ones.

Key Words: Stewart Platform, Manipulators, Hexapod; design, applications, advantages.

A hexapod is a new design of six- legged parallel mechanism structure. Parallel mechanism structures are those ones having parallel links (struts) joining between the its base and its platform, or the output piece. Parallel mechanism generally comprises two platforms which are controlled by a several prismatic joints or legs (struts) acting in parallel. The most common configuration comprises six legs, and these legs are linear actuators such as hydraulic cylinders, or in the case of positive mechanism they could be spring loaded. The output piece is defined as the movable platform which  has six degree of freedom relative to the other platform, which is the base.  With six degree of freedom the movable platform is capable of moving in three linear directions and three angular directions singularly or in any combination.

This type of structure has been known for long time. Around 1800 the mathematician Cauchy  studied the stiffness of the so-called " articulated octahedron". More recently  in 1949, Gough  used similar mechanism for the test of tyres. Then later in 1965,  these mechanisms rediscovered  and used  very widely in the flight simulator by an engineer called D. Stewart. Since that time, any parallel- linkage mechanisms are referred to as  "Stewart platforms"  ,although  Gough discovered this mechanism before him.

A first  parallel mechanism device was used in a robotics assembly cell by McCallion in 1979. Then, Parallel manipulators have been under increasing development over the last few decades, so that they are considered  attractive alternative to the serial linkage devices, such as the conventional robotics arms.

Since that time many improvements and modifications have been done to that  mechanism in order to overcome its restrictive range of motion. Until recently , they created that amazing device which give a wide range of motion besides the advantages of the "Stewart platform".

The initial design of the platform, since the time it was first adopted, requires many changes. Because, the current time is the time of computer controlled devices. In addition, with the advance in the field of robotics, the necessity of inventing positional devices with very high accuracy (may reach sub-micron) has become necessary. Moreover, the old design was yet stiff, but it was limiting the ranges of motions that could be provided from such a design. Therefore,  new techniques of mechanical design; such as: FEA (Finite Elements Method), was introduced to obtain a new family of positional devices with both stiffness and large range of motion.


The hexapod is a closed chain kinematic structure. This mechanical component based on the previously explained structure known as Stewart Platform. As clear from its name, the component has to be composed of six struts. However, there are several combinations that fall under the same name.

TYPE A: The Six Axes Positioner:

The hexapod consists of six struts—hydraulic ones. These struts are free to expand and contract between the base at the bottom, and the top platform. The platform is the output element that gets the 6 DOF of the system. The platform receives all six coordinates freedom in motion. Both ends of the hydraulic struts are connected to either the platform or the base using universal joints. Such a system was first introduced in the flight simulators positioning systems. It started to be commercially available for variety of applications that requires sub-micron accuracy.

Unique Characteristics:
 ·  For any change in the position of the platform along one of the six axis (3 translation, 3 rotation) to be achieved, all the six struts of the hexapod change their position
 ·  Using software control, some models of the hexapod can attain sub-micron accuracy.


The hexapod control: as previously mentioned, any change in one of the struts angle or length, there will be a change in all the other struts. Therefore, the most advanced techniques of Finite Elements Analysis (FEA) and Computer Aided Design (CAD) were employed.

Degrees of Freedom Calculation:

Considering the base to be fixed, the degrees of freedom analysis goes as follow:
 ·  Number of moving parts: 6 hydraulic struts (hydraulic cylinder), which is actually two parts with clearance fit inside each others and the platform.
6 Hydraulic strut 12 parts
1 Platform 1 part
Total 13 parts
 ·  Total DOF of the system = 13 X 6 = 78 DOF
 ·  DOF Analysis:
Number Interface Constraints DOF DOF Type
6 Base: Yoke 1 / Yoke 2 Universal Joint 4   2  RR
6 Strut Lower end (Y2)/Strut upper end (Y3) TR
6 Strut upper end (Y3)/  Platform Universal Joint (Y4) 4 2 RR

TOTAL CONSTRAINTS: 3 X 6 X 4 = 72 constraint
System DOF = 78-72= 6 DOF
The SIX DOF systems goes as follows:
 ·  Three Translations in the three axes (X,Y,Z)
 ·  Three rotations and swaging motions on the three axes.
 ·  No local mobilities or kinematic over-constraints.

Absence of kinematic over constraints can be attributed to the fact that the design does not requires the six struts to be parallel, hence all the basic DOFs exist.


The basic Stewart Platform is made up of six extensible struts, opposing to the previous design, with only one DOF (the cross section is non-circular, does not allow rotation) . The six struts are fixed to the base and the platform using ball-socket joints. This design is dated up to three decades ago; the first design was introduced in 1965 by D. Stewart for use in air craft simulator. This elementary design had some limitations in its range of motion because of such a design.

Degrees of freedom calculation:
Considering the base to be fixed, the degrees of freedom analysis goes as follows:
 ·  Number of moving parts: 13 parts (a platform, six extensible struts and six base struts).
 ·   Total DOF of the system: 13 X 6 = 78 DOF
 ·  DOF Analysis:
Number   Interface                                                     Constraints        DOF        DOF Type
6              Base / Struts: ball and socket joint               3                      3               RRR
6              Base struts / extensible strut lower end       5                      1                 T
6   Strut upper end / Platform: ball and socket joint    3                      3            RRR

TOTAL CONSTRAINTS: 2 X 6 X 3 + 6 X 5 = 66
System DOF = 78-66= 12 DOF
 ·  Since the required DOF of the system is only 6 DOF (TTT, RRR), therefore this implies the existence of local mobilities. By examining the system, the existence of six local mobilities is confirmed between the ball and socket joints on the platform.
 ·  Therefore:
  Calculated DOF = Required/Basic DOF + Local mobilities
           12             =              6  + 6

TYPE C: Proposed Design:
This design was not introduced by any of the companies, but we introduce as trial to eliminate the problem of the six local mobilites that exist in the basic Stewart Platform design. This design follows the same idea of a six legs structure, but with universal joints between the upper ends of the struts and the platform. In addition, the struts only allow one translation DOF (the yokes can not rotate about their axes).
Degrees of freedom calculation:
Considering the base to be fixed, the degrees of freedom analysis goes as follows:
 ·  Number of moving parts: 13 parts (a platform, six extensible struts and six base struts).
 ·   Total DOF of the system: 13 X 6 = 78 DOF
 ·  DOF Analysis:

 Interface Constraints DOF DOF Type
6 3 3 RRR
6  5 1 T
6 t 4 2 RR
Number Interface Constraints DOF DOF Type
6 Base / Struts: ball and socket joint  3 3 RR
6 Base struts / extensible strut lower end 5 1 T
6 Strut upper end / Platform: universal join 4 2 RR

TOTAL CONSTRAINTS: 6 X 3 + 6 X 5 + 6 X 4 = 72
System DOF = 78-72= 6 DOF


I- Flight Simulators:

After the start of the space era in the early sixties of this century, simulation of actual conditions passed by pilots either on planes or space shuttles became a must in order to give the pilots an adequate and necessary training. This is because planes and space shuttles are considered to be "expensive". Not only that, but also because the life of the pilot is equally expensive as the vehicle. The aim of flight simulators is to simulate man/vehicle interaction, through measurement of the pilot readiness and performance and putting a scale for his maneuvering.
The simulator is an actual cockpit mounted on a hexapod. The hexapod is of the "six axis positioner" type, with six hydraulic struts and 12 universal joints distributed on both the base and the platform, which is the cockpit in this case. Such a simulator can be easily modified to simulate a wide range of both ground-based and flight vehicles. Through computer system, the simulator gives a quantitative evaluation for the pilot. From a medical view point, the existence of the body in a 6 DOF system will produce precise simulation on the body's visual and tactile sensors. In other words, the biological effects on the inner ear, and kinesthetic organs ,body's muscle and skin tissue, which are used by humans to sense motion in all directions.
According to McFadden, a company specialized in this type of flight simulators, the benefits of a 6 DOF system on simulation are:
 ·  Enhances realism of the experience
 ·  Increases rider acceptance of simulation
 ·  Virtually eliminates motion sickness
 ·  Improves synchronization of visual and motion information cues
 ·  Able to accommodate more realistic and panoramic visual displays


With the growing interest in quality of produced parts, a new generation of machines that combine high speed, accuracy, stiffness, and multi-axial capabilities started to appear. The basic design of these structures is based on the conventional Stewart Platform. In this case, the machining tool is carried on the platform, hence having the ability to move  six degrees of freedom. There are two possible designs. The first is the one that uses the telescopic struts, hence having universal joints at the end of the strut. The second design is with the ball and socket joint at the end of the strut.
These designs have the following advantages:
 ·  It allows free access to the work zone.
 ·  There is nothing to impede the motion of the machining tool to the work piece.
 ·  Unlike most industrial robots, the hexapod design provides stiffness beyond what the design shows. The struts act longitudinally on the platform, hence producing either tension or compression on it.
 ·  The machine offers micron to sub-micron accuracy. This is because of the software package that is used to control the robot.
 ·  Low friction at the joint, giving long life time for the robot.


Since most medical disciplines, especially in the field of surgery, require high accuracy and controllable forces  when working on human organs, the precision controllers were introduced to the field of medicine as well. Research on the use of hexapod positioners in this field is done by the support of Siemens Medical Engineering. The aim of this robot is to help the surgeon operate on a sub-micron accuracy. This is in order to increase safety in surgeries and prompt further improvement and give a chance for more complicated surgeries.
The use of the robot with hexapod arms enables the high precision and high forces to reach very complicated zones, mostly in the brain because the model was developed for neuro-surgery.

Not only that, on the other side the surgeon will be sitting in the operating cockpit. This is described as the workspace of the future surgeon. The cockpit is mounted on a hexapod platform so that the impression is transmitted to the surgeon for the endoscope going inside the patient. This helps the surgeon to control the tools and give him a feeling of the spatial orientation of the scalpel. As they say, they want the surgeon to "fly through the patient" !
Such a complicated technology is controlled by a computer simulation to avoid errors, where errors are not originally possible!

Other Applications and Research:

  1 -  Fine Positing device for the mirrors of high resolution telescopes.
  2 -  Positioning of optics, electron guns, Lasers, and other energy resources.


              The current paradigm in design and manufacturing involved integration of numerous hardware and sophisticated software in order to create An unique  product of extremely high accuracy . The objective of this integrated product is to enhance quality and reliability, reduce the cost and overall cycle time, and increase flexibility. Hexapod is a dramatic departure from conventional mechanism design; it offers many new attributes for the most manufacturing processes.

* Six degree of freedom
The hexapod consists of six struts which expand and contact between the movable platform,  which carries a spindle, and the fixed platform.  Coordinated motion of these six struts enables the spindle to move in any direction. In addition to the traditional motion in orthogonal axes, X,Y, and Z, this device also is able to move in the rotary complements of pitch, yaw, and roll. This advantage allows the spindle to reach unusual angles and geometrical features.

 * High precision and accuracy
 In contrast to the conventional multi-axis positioning tools, the hexapod technique requires all six struts to alter their lengths if a change of the platform in only one axis is required. On the other hand, if only one strut alters its length, all six coordinates (X, Y,  Z, q, a, j )  will  change. The twelve multi- degree-of-freedom joints must  assure  precision and zero backlash.
              Unlike other multi-axis positioning devices, in which any change in one coordinate influences the position of the pivot point and the other coordinates,  the hexapod can compensate itself automatically. Through the sophisticated software, the coordinate transformations and individual velocity /coordinate information  are transmitted to each motor controller axis.

Computer visualization tools
Due to unconventional design of the hexapod, the  control for the hexapod is through visualizations of the products and the processes by sophisticated software, which  is needed to support extremely detailed visualization. This software package must have " zoom-through" ability; moreover, it should have the ability to scan the whole workplace  through an individual multi-mode system. The advantages of applying such numerical visualization tools  are copious. The actual hexapod will not need to be tied up, freeing it for the other tasks. Safety procedure will be eliminated. A profound set of visual motion data can be attained with minimum human labor; in other words,  this will reduce the human interference and at the same time the human faults.
 *  Graphic simulation and computer animation
Using graphic simulation and animation of the downstream manufacturing process provides a map for the entire workplace envelope. Tool velocity and acceleration data will be  registered for different locations in the workspace and for various speeds and accelerations of the ball- screw struts. Due to extraordinary kinematics of the  hexapod it is predicted that characteristic motion at the tool’s reference frame will be highly dependent on the location in the workspace. Detailed kinematics map will be resolved from the obtained data, identifying regions of the greatest achievable tool velocity and acceleration and those of the lowest. This will give a clear perception of the optimal regions of the workspace for achieving that  most use of different machining process. Ultimately this will promote the development of the hexapod in different manufacturing processes.

*  High stiffness
Besides the various advantages stated above,  the hexapod offers another important feature, which is  the high stiffness and rigidity of its components and all moving parts, such as bearings and joints, and drive screws. This feature results in extraordinary high natural frequencies (500 Hz@10 kg load);consequently, this gives very high speed of cutting and the other maching objectives. In addition, high stiffness of the hexapod’s components  will prevent any bending effect in the six legs or in  the platform, and that what makes the hexapod very  advantageous.

*High load/weight  ratio
The high nominal load/weight is a very important advantage of the hexapod. The  weight of a load in the platform is approximately equally distributed on the six parallel links. That means each link just suffers only from 1/6 of the total weight. Furthermore, under certain load, the struts on the hexapod act longitudinally and therefore exerts either tension or compression on the struts in other words, no axial forces are applied. Consequently, there is no need to design it as massive as the conventional machines.

* Variety in the size
Rotary hexapods can be as small as soda can or as big as 3meters in diameter depending upon the objective of the machine.
Comparing with  the conventional multi-axis machines, the number of parts from which the hexapod is composed is one third fewer which means lighter weight and lower friction.
* Hexapod is  a soft machine
 According to Hexel Corporation, a leading company in hexapod development and production, the hexapod is "a soft machine ." However, that is not in reference to the machining center’s stiffness, thrust, or the other traditional descriptions of the machine tool strength. Soft in the case of the hexapod means that the machine’s accuracy and repeatability are not dependent on its structural alignments. Hexel clarified that by saying , instead  on relying on the ability of the skilled assemblers to scrape in way surfaces and other critical mating points to assure that the base, column, and other components are square and true, a hexapod does not require that kind of  intensive assembly. Its 25- micron accuracy is derived from
mathematical formulas that are the heart of the software that coordinates the relative motions of its six struts.
    He continued, repeatability of the hexapod design is about 10 microns, comes from its need to move a significantly lower amount of mass when machining. Only the spindle motor, cutting tool, and their carrier exert inertia and momentum beyond the servo motors themselves.

 * High production rate
The hexapod can provide higher production  rate in limited time. Since that needs continuos work processing capability, the hexapod  design can accommodate a pallet shuttle system that can automatically move work pieces in and out of the work zone. That can be achieved by designing the machine to be above the worktable.
     In essence, the hexapod design obviously has a great potential in revolutionizing  a host of manufacturing  processes. The merits of such machine are numerous. That providing improved accuracy , stiffness, speed, etc. As a multi processing system those merits will extend beyond individual processing improvements and into a system- oriented  improvements in the manufacturing cell. Reduction in set-up and processing time, and consequently the overall cycle time is one of the most important benefits. High quality and readability will be easily attained through such advanced systems.

       As any new design, hexapod has turned up some problems some of them have been  addressed, and  some still need further developments and refinements.

Friction in the ball joints is  a crucial problem for the hexapod. That the friction coefficient is about 0.8,and that is enough to exert some axial deflection on the struts that influences the accuracy and repeatability. Using a ceramic coating and special lubricant,  the modified struts are down to 0.2  coefficient of friction

Length  of the struts
The length of the struts affects the accuracy of the machine. When the length increases, the accuracy decreases dramatically (possibility of bending). This problem have been overcome by mapping each screw before installing in the machine.

Dynamic thermal growth
This problem has appeared also in the serial linkage mechanism. That with the increase in the speed of  the spindle, there is a dramatic increase in the dynamic thermal growth. One way to overcome that hurdle is by monitoring the struts in real time employing one dimension finite element analysis  that activates an automatic error compensation routine built into the software and based on the known growth rate of the struts.

The accuracy of the parallel- mechanism is not only dependent upon an accurate control of the length of its links but also upon  a knowledge of its geometrical characteristics. According to the fabrication tolerances many factors will play a role in the final accuracy of the machine. Up to 132 parameters must be specified to describe the geometrical characteristics of the mechanism which seems to be very difficult to adjust all parameter. Therefore the calibration of the hexapod still an open problem.


An example for milling machine that uses one kind of hexapod joints. The 6 DOF decreases the machining time required by the machine to perform machining in very fine positions, with outstanding quality of machining.
The hexapod joint when used in flight simulators. The above platform acquires 6 DOF, which exactly simulates air craft experience.
The basic Stewart Platform, with ball and socket joints at both ends of the strut. This system has six local mobilities.
The hexapod initial design put by D. Stewart.
Applications of Hexapods in milling machines.