What is a parallel robot?

Robot manipulators can be either serial or parallel

A serial robot from Mitsubishi Electric.
A serial robot from Mitsubishi Electric.

According to the International Organization for Standardization (standard ISO 8373:2012), a robot is an "actuated mechanism programmable in two or more axes with a degree of autonomy, moving within its environment, to perform intended tasks."

Loosely speaking, a serial robot is a set of bodies (called links) connected in series through actuated joints, which are typically either revolute (i.e. rotating) or prismatic (i.e. translating). One extremity of this serial chain of links is called the base and the other the end-effector. Serial robots are also called robot arms. Most industrial robots are serial. Although some of them contain parallelogram linkages (e.g. robot palletizers), they are still referred to as serial robots.

A parallel robot from Mitsubishi Electric.
A parallel robot from Mitsubishi Electric.

In a parallel robot, the end-effector is connected to the base through several chains of interconnected links. In other words, a parallel robot has at least two "legs" (or "arms"). Most of its joints are not actuated, and many of these passive joints have several degrees-of-freedom (DOFs) (e.g. spherical, universal, and planar joints).

Two of the most popular parallel robots are the telescoping-leg hexapod used in most motion simulators (often called "motion platforms") and the so-called Delta robot, generally used for rapid pick-and-place. While there are fewer parallel robots than serial robots in use, the variety of parallel robots is larger.

The origins of parallel robots

Possibly the first spatial parallel robot, invented in 1928 (US Patent No. 1,789,680).
Possibly the first parallel robot, invented in 1928 [1].

A five-bar parallel robot invented in 1934 (US Patent No. 2,213,108).
A five-bar parallel robot invented in 1934 [3].

Theoretical work on parallel mechanisms, and particularly hexapods, dates back centuries, when English and French geometricians were particularly interested in polyhedra. However, possibly the first parallel robot was conceived by James E. Gwinnett, a farmer(!) in the USA, who applied for a patent in 1928 [1]. His invention was a 3-DOF spherical motion platform for use in movie theaters, where sound and picture were still a novelty.

A decade later, and only seventeen years after the term "robot" was coined by Karel Čapek, a new parallel robot was invented for automated spray painting by Willard L. V. Pollard [2]. This ingenious invention was a 5-DOF triple-arm parallel robot. Pollard's robot was intended for spray painting, but, unfortunately, was never built. The engineer who co-designed the first industrial robot was Willard L. V. Pollard's son, Willard L. G. Pollard Jr. (if we don't count the Meccano robot crane built by Griffith P. Taylor in 1938).

In 1934, Willard L. G. Pollard Jr. filed a patent for a spray painting machine [3]. The invention comprises a control system and a manipulator. The control system consists of perforated films, and the manipulator is essentially a five-bar linkage.

Pollard Jr. licensed his invention to the DeVilbiss company in 1937. In 1941, DeVilbiss, later to become the first industrial robot manufacturer, completed a prototype of a spray painting robot [4]. However, this was a serial robot, and used only the control system proposed by Pollard Jr.

The first octahedral hexapod or the original Gough platform at birth in 1954.
The first octahedral hexapod, the original Gough platform, was built in 1954.

In 1947, on the other side of the Atlantic, a new parallel robot was invented, the one that became the most common parallel robot, the telescoping-leg hexapod. Dr. Eric Gough, who built this first octahedral hexapod, was a distinguished automotive engineer at Dunlop Rubber Co. in England [5].

Called the "universal tyre test machine", this robot was invented to address the problems associated with aircraft landing loads. A universal machine was needed to determine the properties of tires under combined loads. But the octahedral hexapod was not invented from scratch. At that time, as Dr. Gough points out in [5], systems with three vertical and three horizontal jacks were already very common. These hexapods had become very popular because "the jack adjustments [were] simple and interpretable" for small variations. Systems of this type are known by the acronym MAST, which stands for Multi-Axis Simulation Table, and are still manufactured today.

The new feature introduced in Gough's platform was the symmetrical arrangement of the six legs. The machine was built in the early 1950s and was fully operational in 1954. In the early days, the extensible legs were manually adjustable.

The first flight simulator based on an octahedral hexapod as in the mid 1960s.
The first flight simulator based on an octahedral hexapod pictured in the mid-1960s (courtesy of Klaus L. Cappel).

Apparently, Gough's work remained unknown for more than a decade. Back in the USA, Menahem Suliteanu and William R. La Valley had filed a patent application in 1962 for a 6‑DOF antenna support consisting of three tripods [6]. Then, in 1965, Everett R. Peterson, filed a patent application for an octahedral hexapod with double-ball joints [7]. His application was, however, preceded by a few months by the application of Klaus L. Cappel of the Franklin Institute for what later became one of the most important patents in the history of parallel robots [8]. Cappel's motion simulator idea resulted from a request by the corporate office of the Sikorsky Aircraft Division of United Technologies for the design and construction of a 6-DOF helicopter flight simulator. This was the first ever flight simulator based on an octahedral hexapod.

The first license was granted to Link, then the foremost manufacturer of flight simulators, in the late 1960s. The first infringement was committed in the early 1970s by CAE, the current leader in flight simulators. The lawsuit launched by the Franklin Institute was successful, resulting in a penalty and a forced license. Other companies subsequently entering the market had to respect Cappel's patent. Meanwhile, two other motion simulators were built by the Franklin Institute. The first was a helicopter simulator. The second was a driving simulator.

Schematic of the one and only Stewart platform.
Schematic of the one and only "Stewart platform" [9].

Back in the UK, in 1965, a mechanical engineer, D. Stewart, unaware of Gough's and Cappel's work, proposed a mechanism with six telescoping legs for use as a flight simulator [9]. His parallel mechanism, however, is different from the octahedral hexapod, which is, paradoxically, often referred to as the "Stewart platform". Stewart's paper sparked ardent discussions among researchers, one of whom was Dr. Gough, who reminded them of the existence of his tire-testing machine. Various suggestions for the use of the hexapod were made, many of which were accurate predictions of future uses.

Although Stewart was neither the inventor of the octahedral hexapod nor the precursor of today's six-legged flight simulators, there is no doubt that his paper had a tremendous impact on subsequent development in the field of parallel robots. In fact, because of it, Cappel had to reissue his patent, restricting its scope.

The first ever Delta robot, developped in 1985.
The first ever Delta robot, developed in 1985 (courtesy of Reymond Clavel).

For nearly two decades, parallel robots attracted very little attention, but, in the early 1980s, their popularity suddenly started to grow (see [10]) and has never stopped. In 1985, for example, Donald C. Fyler, from the Charles Stark Draper Laboratory (USA), came up with the idea of using a five-bar mechanism as a robot [11]. He claimed that this double-arm robot was a better alternative to the SCARA robot that had been invented in 1979 by Prof. Hiroshi Makino.

Since the early 1980s, hundreds of novel designs have been proposed, and almost as many applications filed [12]. Many of these parallel architectures are truly innovative, but there was one that became by far the most sucessful parallel robot for industrial application: the Delta robot.

In the summer of 1985, Prof. Reymond Clavel (now retired) from the EPFL, Switzerland, came up with the brilliant idea of using parallelograms to build a 4-DOF parallel manipulator for high-speed pick-and-place operations. He applied for a series of patents, based on which the author of [13] and several companies, including ABB, eventually obtained licenses to manufacture his invention. During the life-span of his key patents, more than 10,000 units were manufactured. Today, the Delta robot design is no longer protected and dozens of companies offer their own pick-and-place versions, including FANUC, Motoman, and Kawasaki.

What is so special about parallel robots?

A 6-DOF precision positioning tripod.
A 6-DOF precision positioning tripod by SmarAct.

It is often said that parallel robots are stiffer, faster, and more accurate than serial robots. The truth is much more complex, however, since parallel robots differ hugely from one another.

Moog's MB-EP-6DOF/60/14000KG motion base, for example, can move up to 14,000 kg, while KUKA's KR 1000 1300 TITAN PA industrial robot, one of the strongest serial robots, can lift only 1,300 kg. The reason for this disparity is that the legs of a hexapod are not subjected to bending or twisting, but this is not the case for many parallel robots, nor is it always true that the payload in a parallel robot is supported by several legs.

It is true that the motors in many parallel robots are fixed to the base, which leaves the mobile part relatively light. This has made Delta robots the fastest robots that have been designed for years now. However, recent advances in motor technology and control have produced serial robots that are extremely fast.

The Exechon PKM.
The 5-DOF Exechon PKM by Exechon.

Finally, it is true to say that most multi-axis precision positioning devices are based on parallel robots, mostly hexapods and tripods. However, the reason for this has less to do with the fact that errors in a serial robot accumulate, whereas they are averaged in a parallel robot, and more to do with the fact that hexapods and tripods are rigid [15].

The real merit of parallel robots is that there are hundreds of possible architectures, each with very specific advantages and disadvantages. Some parallel robots are perfect for machining (they are called Parallel Kinematic Machines or PKMs) or for motion simulation, because they are rigid. Others are great for pick-and-place operations, because their mobile part is light. Cable robots, for example, are ideal for covering a very large work area, such as a stadium.

There are currently more than a million industrial robots in operation, and the vast majority of them are serial. In fact, there are probably no more than 50,000 parallel mechanisms with 3 or more DOFs. However, this situation will most likely change.

Who manufactures parallel robots and for what applications?

The Quattro by Adept Technology.
The 4-DOF Quattro robot by Adept Technology.

Dozens of companies currently offer parallel robots, mostly hexapods and Delta robots. In the case of motion simulation, one of the three most popular applications for parallel robots, the industry leader is Moog, which has sold more than 1,400 motion bases. Another major supplier of motion systems is Bosch Rexroth. There are dozens of other smaller builders, such as InMotion Simulation and Servos & Simulation.

The second most popular application for parallel robots is the pick-and-place operation. Of course, Delta robots are mostly used for this purpose. These are now manufactured by ABB, FANUC, Kawasaki, Motoman, Panasonic, and dozens of smaller manufacturers around the world. There is, however, a new trend, towards four-arm 4‑DOF pick-and-place robots, which began when Adept Technology produced their incredibly fast Quattro [17]. The Veloce, from Penta Robotics, is another robot of this type. Finally, Codian Robotics and VELTRU manufacture both standard and dual-arm Delta robots, while Electro ABI offer asymmetric three-arm Deltas.

The W5D haptic device by Entact Robotics.
The 5-DOF W5D haptic device by Entact Robotics.

The third most popular application for parallel robots is precise positioning. Most of these robots are based on telescoping-leg hexapods, but tripods and hexapods with fixed-length legs are used as well. The major manufacturers of hexapods for high-accuracy alignment are PI, Symétrie, and Newport. Other manufacturers are SmarAct and ALIO Industries.

Parallel mechanisms are also the preferred choice for haptic devices, which devices are manufactured by Force Dimension, Entact Robotics, and Novint, for example. Novint's Falcon $250 game controller is an extraordinary example of how parallel mechanisms can be found everywhere.

There are also several machine tools based on parallel mechanisms. Most PKMs are built by the Starrag Group, by Metrom and by licensees of Exechon. Finally, there are companies offering various products based on parallel robots, from CMMs (e.g. Renishaw) to toys (e.g. IXI-Play).

Are parallel robots difficult to design?

The Hexapteron invented by Nicholas Seward.
The Hexapteron 3D printer developed at the ÉTS [14].

These days, coming up with yet another parallel robot design is not easy. Hundreds of designs have already been patented, and it is difficult to optimize an existing design. However, developing a parallel robot for an undemanding application (e.g. slow material handling or 3D printing) is relatively simple.

In fact, to design a robot that can follow prescribed trajectories with its end-effector, all that is required is to solve its inverse kinematics. This involves calculating the required motor positions (active-joint variables), given the pose (position and orientation) of the end-effector. For a typical parallel robot, this is straightforward. For example, the inverse kinematics of the telescoping-leg hexapod boils down to finding the distance between the attachment points of each leg. In the case of the Hexapteron [14], the inverse kinematics is basically ρ1 = xP1, ρ2 = xP2, ρ3 = yP3, etc., where ρi (i = 1, 2, ..., 6) is active-joint variable i, and xPi is the x coordinate of the center of platform joint i, etc. The inverse kinematic equations often degenerate at so-called Type 1 singularities. singularities, which are configurations where the end-effector is constrained in some directions, even if all the motors are deactivated.

The workspace of ABB's FlexPicker
The workspace of ABB's IRB 360 (FlexPicker).

The workspace of the robot then needs to be calculated. There are several advanced methods for doing this, but a simple discretization method can also be used. With this method, the inverse kinematics are solved for each potential pose of the end-effector, and the designer verifies that all the constraints are satisfied. For most robots, there are several possible inverse kinematic solutions, also called working modes, that can be used. For multi-DOF parallel robots, the workspace is usually impossible to represent graphically, and so it is common in this case to calculate only the constant-orientation workspace.

A major problem with parallel robots is the presence of Type 2 singularities. These are dangerous configurations where the end-effector is no longer fully constrained. In some parallel robots, they are simple to describe (e.g. in the five-bar, these occur when the distal links are aligned), but in most robots they are very complex to analyze. Type 2 singularities must be taken into account when computing the workspace, since they are difficult to cross and they cut the workspace into sections. Ideally, the mechanical limits of the parallel robot should prevent it from entering a Type 2 singularity.

A 3-DOF nanopositioning tripod by ALIO Industries.
A 3-DOF nanopositioning tripod by ALIO Industries.

In some applications, such as coordinate measurement or rapid material handling, the direct kinematics of a parallel robot also need to be solved. This involves calculating the possible poses for the end-effector, given the active-joint variables. For some parallel robots, this task is trivial (e.g. for the Tripteron), for others it is relatively simple (e.g. for the five-bar robot, the Delta robot, or even the Hexapteron [14]), but for most it is very challenging. For example, the direct kinematics of the Tripod built by ALIO Industries boils down to solving a univariate polynomial of degree 4 [16]. However, this polynomial is of degree 40 in the case of the telescoping-leg hexapod [12], which means that the hexapod can have up to 40 different solutions to its direct kinematics, called assembly modes. For this reason, a numerical iterative method is most often used to solve the direct kinematics for a single assembly mode.

Finally, as with any other mechanism, parallel robots need to be optimized. Since the performance of most parallel robots varies significantly from one pose to another, and since most performance criteria are antagonistic, the optimal design of most parallel robots is a very difficult problem. Unfortunately, there is no one procedure for optimizing parallel robots, and they all have their pitfalls.

Where to find further information about parallel robots

Textbooks on parallel robots.
Textbooks on parallel robots.

Plenty of information about parallel robots is available at ParalleMIC, a website established and maintained by Prof. Ilian Bonev. However, his Twitter account (@ibonev) is the ultimate source for news concerning everything related to parallel mechanisms (and industrial robots in general). Finally, the website of Dr. Jean-Pierre Merlet of INRIA provides an extensive bibliography of research papers related to parallel mechanisms, as well figures depicting many parallel robot designs.

Unquestionably, one of the leading textbooks in the field is Dr. Merlet's Parallel Robots. There are several other more recent books as well. In addition, hundreds of scientific papers have been published in journals like Mechanism and Machine Theory and the Journal of Mechanisms and Robotics, where most of the information is available, and there are numerous theses and dissertations around the world that can be consulted. However, no amount of reading can take the place of experimenting with a real parallel robot like DexTAR.


  1. Gwinnett, J.E., "Amusement device," US Patent No. 1,789,680, January 20, 1931. Download PDF
  2. Pollard, W.L.V., "Position controlling apparatus," US Patent No. 2,286,571, June 16, 1942. Download PDF
  3. Pollard, W.L.G., "Spray painting machine," US Patent No. 2,213,108, August 26, 1940. Download PDF
  4. Roselund, H.A., "Means for moving spray guns or other devices through predetermined paths," US Patent No. 2,344,108, March 14, 1944. Download PDF
  5. Gough, V.E. and Whitehall, S.G., "Universal tyre test machine," Proceedings of the FISITA Ninth International Technical Congress, pp. 117-137, May, 1962. Download PDF
  6. Suliteanu, M. and La Valley, R., "Antenna support," US Patent No. 3,229,941, January 18, 1966. Download PDF
  7. Peterson, E. R., "Movable and rotatable top," US Patent No. 3,288,421, November 29, 1966. Download PDF
  8. Cappel, K.L., "Motion simulator," US Patent No. 3,295,224, January 3, 1967. Download PDF
  9. Stewart, D., "A platform with six degrees of freedom," Proceedings of the IMechE, Vol. 180, Pt. 1, No. 15, pp. 371-385, 1965-66. Download PDF
  10. Fichter, E.F., "A Stewart platform-based manipulator: General theory and practical construction," The International Journal of Robotics Research, Vol. 5, No. 2, pp. 157-182, 1986. External link
  11. Fyler, D. C., "Control arm assembly," US Patent No. 4,712,971, December 15, 1987. Download PDF
  12. Merlet, J.-P., Parallel Robots, Springer, 2nd edition, 2006. External link
  13. Clavel, R., "Device for the movement and positioning of an element in space," US Patent No. 4,976,582, December 11, 1990. Download PDF
  14. Seward, N. and Bonev, I.A., "A new 6-DOF parallel robot with simple kinematic model," IEEE International Conference on Robotics and Automation (ICRA), Hong-Kong, China, 2014.
  15. Briot, S. and Bonev, I.A., "Are parallel robots more accurate than serial robots?," Transactions of the Canadian Society for Mechanical Engineering, Vol. 31, No. 4, pp. 445-455, 2007. External link
  16. Bonev, I.A., "Direct kinematics of zero-torsion parallel mechanisms," IEEE International Conference on Robotics and Automation (ICRA), Pasadena, CA, USA, 2008. External link
  17. Nabat, V., Pierrot, F., Mijangos, M.D.L.O.R., Arteche, J.M.A., Company, O., and Armentia, K.F.P.D., "High-speed parallel robot with four degrees of freedom," US Patent No. 7,735,390, June 15, 2010. Download PDF