In article 3 of 8 in our Motion Series of articles, Cruden’s Martijn de Mooij and Dennis Marcus take a look at the factors to consider when adding further degrees of freedom to increase the workspace in a driving simulator.
Driving simulators exist in many shapes and sizes. The motion system is no exception to this rule, and a wide variety of system designs exist. Generally speaking, motion systems can be classified as: parallel motion systems, serial motion systems, or cascaded systems, which may be a combination of parallel and serial components. At Cruden, we are often asked about the possibilities to extend a 6-DOF hexapod motion system with additional degrees of freedom. In this article, we elaborate on the main considerations regarding adding complexity to the motion system of a driving simulator. We discuss some kinematic, mechanical, and dynamical factors, as well as workspace management.
First, let’s define what we mean when we say parallel, serial and cascaded.
The Stewart platform – or hexapod – is a typical example of a parallel motion system. It is frequently at the heart of a driving simulator. In a parallel motion system, all actuators work together to create platform motion in every degree of freedom. That is, all six actuators may change length when the platform is moved forward, whilst the same six actuators change length when it is moved to the left.
In a serial motion system, the platform is moved through chosen degrees of freedom by a chain of actuated (1-DOF) mechanisms, each typically driving a specific degree of freedom. This simple example illustrates the serial attribute of the system: for a 3-DOF system, a sled could be moved in “X” relative to the world by actuator #1. On top of the sled, a slider system is placed in the “Y” direction, accommodating an actuated hinge that applies roll to the end effector or driving simulator platform. Even though all actuators move simultaneously in normal operation, one may see the motion as being applied as a longitudinal-lateral-roll sequence.
We refer to a cascaded system if autonomous systems are ‘stacked on top’ of each other.
A cascaded system is often built to increase the available motion range in one or two particular degrees of freedom where they are important for the specific driving task to be performed. For example, if the simulator is intended for city driving, a yaw table is stacked on top of a hexapod to properly simulate 90 degree turns (see our previous article about driving simulator workspace). Or, if the simulator is intended for highway driving, a lateral rail is added below the hexapod to enable lane-change maneuvers based on position cueing, rather than filtered acceleration cueing with a washout.
Kinematic aspects
Cascaded motion systems seem to be very simple from a kinematic perspective when it comes to extending the motion space. But appearances can be deceiving! It certainly looks like adding a linear rail to a hexapod simulator will greatly increase its lateral or longitudinal motion capabilities. Do you want a bit more yaw range? Then add a 360 degree yaw table to achieve infinite yaw motion. But be careful, this is only true in theory.
Imagine, for example, a motion system that consists of a long lateral rail with a yaw drive and hexapod stacked on top. If the platform is rotated in yaw, movement of the lateral rail is no longer perceived by the driver as pure lateral motion! Instead, it is perceived as a combination of lateral longitudinal motion. This ‘parasitic’ longitudinal motion needs to be compensated by the longitudinal motion of the hexapod. If the longitudinal workspace of the hexapod cannot compensate sufficiently, then a lot of lateral range is left unused, unless you are willing to accept a strong yaw washout and trade yaw motion for lateral motion.
This issue can be solved by cascading an additional linear motion system for the longitudinal direction, but only partly because the ability of the longitudinal rail to compensate for the parasitical motion, depends on the position of the longitudinal rail in the workspace. If you are driving up to a turn while braking hard before turning in, the ability to compensate the parasitic longitudinal motion will be limited because a large part of the longitudinal workspace was used to simulate the deceleration.
Increasing workspace by cascading motions systems certainly has its benefits, but it is important to be aware of the limitations as well.
Laws of physics
When it comes to mechanical complexity, a motion system that only consists of a hexapod has several clear advantages over a cascaded system.
The main advantage is related to mass, the m in Newton’s Second Law. Driving simulators – especially high-performance simulators – have to be agile and produce rapid, high-frequency motions that involve large accelerations.
Given that the maximum force of an actuator is limited, the lower the mass you have to accelerate, the higher the acceleration experienced by the driver; F = ma.
In cascaded systems, each actuator has to accelerate the mass of its own moving platform and the mass of the actuators, while supporting the structures of the degrees of freedom that are stacked on top of it. For example, the actuators of the linear rail of the Daimler simulator in Sindelfingen do more than just accelerate the simulator cabin; they have to accelerate the entire hexapod as well. Thus, a lot of F is necessary to obtain sufficient a, simply because m is very large!
Mechanical aspects
The mechanical connections between the motion systems in a cascaded setup will introduce play, which has to be dealt with in order to maintain precision and an acceptable frequency response. The more systems you stack on top of each other, the more challenging this will get, especially since a small portion of backlash at the root will be amplified through the chain of stacked mechanisms. Thus cascaded systems are typically more complex and expensive from a maintenance point of view. With six identical actuators, a hexapod-only system, is an elegant and dependable motion concept.
Dynamical aspects
When looking at the performance specifications of cascaded systems, one might assume that the performance numbers of each subsystem can simply be ‘added up’ to get the performance number of the total system. This is true for the position and velocity numbers, but definitely not for the acceleration numbers!
The acceleration performance of two systems stacked on top of each other in a cascaded system cannot simply be added together, because for every action there is an equal and opposite reaction. The force required to accelerate the second system needs to be reacted by the actuators of the first system, and thus the actuators of the first system need to work a lot harder, particularly if the second system is also accelerating the platform in the same direction. It is more reasonable to assume that the maximum acceleration of the system is simply equal to the largest acceleration of either of the sub-systems. The same applies to the frequency responses.
The cable simulator recently introduced by VI-grade is equipped with a unique active inertia compensation system to cleverly maintain as much of the dynamic performance of the 6-DOF parallel motion system – carried by the disk frame – as possible. Subsystems like this add to the complexity of a cascaded system but they are a necessity in cascaded motion system designs.
Our advice: add degrees of freedom where they are needed
It is our opinion that a driving simulator should always be built according to its intended use. The motion requirements for a Formula 1 simulator are completely different to the simulator designed to assist interior design validations at an automotive OEM
When running driving simulator experiments in a city environment that demands lots of tight turns, a hexapod alone might not deliver the desired driving experience. Adding a yaw table below or above the hexapod to achieve full, 360° yaw could make sense in such a case, as Cruden is doing for several of the driving simulators at BMW Group’s new FIZ Driving Simulator Centre in Munich.
For highway lane-change maneuvers involving ADAS, a lateral rail could be a valuable addition – as seen at Daimler’s highway-focused simulator in Sindelfingen, which employs a hexapod moving on a lateral rail to provide generous workspace in the sway direction. These cascaded setups can also help the hexapod’s actuators to preserve their workspace in the other DOFs, leading to more realistic motion.
The innovation in hexapods has been continuous over the years. Cruden now also offers an octopod solution: a ‘hexapod’ with eight legs. This will be explored further in a future article. Featuring two additional actuators resulting in less load across more actuators, this parallel system brings dramatically increased stiffness over the hexapod and higher performance in general. It might seem more complex from a kinematics point of view, but in the same way as the standard hexapod, the user can simply send vehicle acceleration to the system and Cruden can take care of the rest.
Conclusion
When considering whether to purchase a cascaded motion system or a parallel system, there is no reason to automatically favor one type over the other. The best option, as always, will depend on the use cases for which the simulator is intended: what is it that the driver in the simulator should experience, and how is that best achieved? Even extending the workspace in one DOF can result in a choice of configurations, such as mounting a yaw table on top of the hexapod, or vice versa, depending on the simulator’s purpose. In some use cases, increased stroke in one DOF might outweigh a loss in stiffness, whereas in another case a reduction in costs and spare parts is more important than anything else. In the end it is all an engineering trade-off with many permutations to consider. The right solution for your needs is out there and we are happy to help you find it.
For more information, please contact Dennis Marcus via d.marcus@cruden.com or on +31 20 707 4646.
Links to subsequent articles will be added below as they are published.
View all articles in our Motion Series of articles: here.
Article 1: Driving Simulator Motion Systems 101
Article 4: Motion for immersion VS motion for vehicle dynamics and motorsport
Article 5: Good Vibrations: Using a Driving Simulator for NVH development
Article 6: Acceleration is not enough: there’s more to accurate motion cueing than meets the eye
Article 7: A real car in a virtual world: the pros and cons of chassis mockups in driving simulators
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