This paper presents the results of a computer optimising a multibody system using Generative Design methods to select a lower-cost actuator that meets process requirements with its parameters. Optimisation was performed to reduce the mass of the motion apparatus components of the author's CPM device, used for the rehabilitation of patients after knee arthroscopy and total or partial knee replacement. An analysis of the kinematics and dynamics of the multibody mechanism, based on a virtual model, was carried out to identify the requirements for selecting an actuator. The main components of the motion apparatus mechanism were subjected to a series of numerical analyses using selected CAD/CAE tools, with the assumed criterion of varying material and component shapes to ensure that the required strength and accuracy of the mechanism links were maintained, assuming the same functionality. The results of the numerical analyses will be the basis for the selection of the optimum solution, for which a new, lower-cost actuator will be selected.
Keywords: positioning system; CPM device; arthroplasty; CAD/CAE; generative design; actuators selection
An active lifestyle, especially professional sport, which puts a heavy strain on the musculoskeletal system, as well as civilization-related diseases that are usually associated with a lack of physical activity, such as obesity, diabetes, etc., all contribute to damaging the knee. The knee is the largest joint in the human skeleton. Because of its complex structure and the stresses of everyday movement, it is highly susceptible to injury. Diseases and injuries of the knee joint generally exclude or severely restrict people from performing their daily activities due to the impaired motor function associated with a reduced or lost ability to move fully or partially. The main complaints in the knee joint are usually associated with meniscus injuries, sprains or dislocations, and damage to the cruciate ligaments. These conditions are usually temporary and can be reversed with appropriate rehabilitation. Many times, in order to make a proper diagnosis, a procedure is practiced to view the knee joint, called arthroscopy. Chronic joint inflammation is much more problematic from a rehabilitation point of view. This can be caused by advanced osteoarthritis of the knee or rheumatoid arthritis. The joint surfaces that cover the bones, which have been lost or mechanically damaged, need to be replaced in whole or in part by artificial implants that precisely restore motor function and eliminate pain. The treatment uses total endoprostheses, single-compartment endoprostheses, or bicompartmental endoprostheses. The medical procedures used to replace a total or partial knee are called total or partial knee replacement (also called knee arthroplasty) [[
The above surgical procedures cause patients discomfort after surgery due to pain, swelling, and tenderness of the joint. Patients' limitation of motor function due to joint pain paradoxically leads to an increase in stiffness and thus a reduction in the initial mobility within the joint (Range of Motion—ROM). Most physio-therapists recommend continuous passive motion (CPM) devices immediately after knee surgery. Continuous passive motion (CPM) is a rehabilitation therapy that uses a machine to move a joint for a patient [[
Various modifications of the CPM device are being used in many research centres around the world for mechanical kinesitherapy of various human upper and lower limb joints [[
This paper was written in response to an engineering need to optimise the design of the motion apparatus of a CPM device using modern CAD/CAE tools and Generative Design methods, which are a form of artificial intelligence that use the power of the cloud and machine learning to speed up the whole process starting from design to execution [[
The use of the CPM device in kinesitherapy immediately after surgery and during the subsequent recovery period after knee arthroscopy or endoprosthetic is a common practice in many medical facilities. Continuous passive motion is designed to improve the ROM of the knee joint. This will consistently reduce pain. It is assumed that by bending the limb in a range of 90 to 106 degrees, it is possible to perform basic activities, including movements such as descending stairs, rising from a toilet or low chair, and tying shoes [[
The existing body of knowledge on CPM research is mainly concerned with the validity of the use of CPM devices and determining the possible benefits for the patient's health. The vast majority are scientific papers, mainly of a strictly medical nature [[
The technical solution of the motion apparatus presented in this study is unique. This is due to how the positioner motor of the CPM device is driven. A slider–crank mechanism coupled to an electric actuator was used [[
The content of this paper is structured as follows: (
The design optimisation study will be carried out using Generative Design methods. It will focus on the main positioner of the CPM rehabilitation device. The research object will be a virtual model of the CPM device developed in the SolidWorks 2023 software environment. The main dimensions of the device components were taken from an analysis of design guidelines for this type of biomedical solution, based on an atlas of human measurements and data for ergonomic design and evaluation [[
The supporting structure of the CPM unit (
The CPM has two independently controlled platforms, mainly used to support the patient's feet (
The movable links of the main positioner are fixed to the support structure on the patient side and are movable on the other side using a movable sliding guide (
In order to be able to approach the problem of optimising the positioner design according to the criterion of reducing the mass of the links forming the structure of the kinematic chain using Generative Design methods, a preliminary numerical study was carried out for this purpose in the ANSYS Workbench 2022R2—Rigid Dynamics toolbox [[
For the CPM numerical analyses, a simplified test model was prepared based on the geometry previously modelled in SolidWorks 2022, which was the basis for further analyses in ANSYS Workbench 2022. Simplifications were made to the computer model by removing process chamfers and roundings, eliminating holes for connecting elements that attach the motion apparatus to the structure's support frame, and replacing bolted connections with fixed mates. These modifications were duly justified so as not to compromise the quality of the final test result while at the same time speeding up the numerical calculations. Figure 2 shows the kinematic structure of the single-limb positioner.
Figure 2 also shows the components of the positioner. We can distinguish between them: (a) links (
A summary of the masses of each joint and element is highlighted in Figure 1 and an indication of the material of manufacture of the joints is given in Table 1.
The study of the design of the motion apparatus to optimise the solution for reducing the mass of the main components that make up the positioner of the CPM device, and finally the selection of a new actuator for the positioner drive system, was divided into several stages. In the first stage, a kinematic analysis of the motion apparatus mechanism of the CPM positioner will be performed, using the Rigid Dynamics toolbox of ANSYS Workbench 2022R2. This allows the determination of displacement, velocity, and acceleration values in specific kinematic pairs. These parameters will be defined for the geometry of the virtual model output previously designed in SolidWorks. As a result of the analysis, we obtain the parameters of the characteristic points of the mechanism. In the second stage of the study, the dynamic parameters of the mechanism will be determined—kinetic, potential, external (this is all the energy the loads and joints bring to a system [[
To analyse the kinematics of the CPM device, a scenario corresponding to the real use of the device was assumed. After defining the kinematic pairs in each link joint (link 5 is permanently fixed to the ground and is a fixed link; a rotational kinematic pair A' is defined between links 5 and 3; links 3 and 4 form a rotating pair D'; a rotating pair E' is defined between links 4 and 6; the linear guide car 6 together with the guide form a translational pair F'; between the linear electric actuator 9 and the calf support 8, a fixed stationary connection G' is defined; similarly, connections are defined between links 9 and 11, i.e., the actuator and the link of the Delta robot—H' and between 10 and 11, i.e., the link of the robot and the platform supporting the patient's foot—kinematic pair I'—as these kinematic pairs are excluded from further analysis; link 1 forms a rotating pair B' with the ground and is connected on the other side to link 2, forming a rotating pair C' with it; link 2 is connected to links 3 and 4 by a rotating pair D'; the thigh and calf supports are permanently attached to links 3 and 4 and this connection is defined as fixed); all components of the combined mechanism are positioned in the configuration shown in Figure 2B. The starting position defined in this way allows the lower limb to be positioned and fixed to the movement apparatus of the CPM device. The mechanism analyses did not include the mass and impact of the elastic bands used to attach and secure the limb to the thigh, calf, and foot supports (Figure 1, Detail 10). The actuator is attached to link 1 and forms with it a rotating pair B'. The operating mode of the device includes the speed of the actuator, which can be set to 4, 2, or 1 rpm. For the analysis, a variant of actuator movement was assumed with a maximum speed of 4 rpm (i.e., 24°/s), in the angle range 0° → 157° → 0° → −3°→ 0°. For the most part, this covers a regular range of motion of the knee (from −10° to 155°) [[
Displacements of the Delta robot's end effector (the platform that supports the patient's foot) were not included in the analysis. During the robot's motion phase, the support platform is assumed to be in a fixed position throughout the motion and is therefore not considered further. The finite element mesh required for numerical analysis is automatically generated by the CAE tool. For this type of study, this is of little importance as the final result does not depend on the accuracy and type of mesh chosen.
For the dynamic analysis of the limb positioning mechanism of the CPM device, CAE studies were also carried out using the Rigid Dynamics toolbox of ANSYS Workbench. A scenario similar to the kinematic analysis has been assumed for the definition of the drive operation, i.e., resulting from the rotation of the drive link in the range of angles: 0° → 157° → 0° → −3°→ 0° with velocity 4 rpm (i.e., 24°/s). The effect of gravity force (9806.6 mm/s
The optimisation of the links (Figure 2—(
The same procedure as described above for links 3 and 4 is used to optimise the mass of the drive mechanism links (Figure 2—(
The finite element size used to perform the Generative Design analyses was 3 mm and the finite element mesh was 23,012 finite elements for link 3. For link 4, the finite element size was 3.3353 mm with the same number of finite elements, i.e., 23,012. For link 4, the finite element size was 3.3353 mm, with the same number of finite elements, i.e., 23,012. The choice of these values was dictated by the optimum settings suggested by the Creo Parametric software, which ensured the shortest possible generation time for the new structure while maintaining a high-quality result.
This section describes the results of the numerical analyses carried out in ANSYS Workbench and Creo Parametric, which will form the basis for selecting a smaller (cheaper) and more suitable actuator to drive the CPM device positioner.
Mathematical equations describing how to solve the forward kinematics of the CPM mechanism are derived and detailed in Trochimczuk et al. [[
The graph shows the changes in the kinematic parameters excluding the Z-axis which, due to the flat nature of the mechanism, has a constant value and is irrelevant for the purposes of the analysis, so it was deliberately omitted. The analysis was carried out assuming maximum actuator speed. In rehabilitation practice, such speeds can only be applied in the final stages of rehabilitation, when the ROM in the knee has already been deepened. The actual actuator velocity values at the beginning of the rehabilitation process are four times lower, so the obtained parameter values are also four times lower than those shown. The above comment applies to all kinematic analysis results presented below.
When analyzing the result in Figure 3, special attention should be paid to the maximum value of the X-axis velocity, which is 8.8897 × 10
Figure 4 shows the results of the kinematic analysis for the kinematic pair D' of the positioner mechanism of the CPM rehabilitation device. Consideration of this kinematic pair is very important because it is through this kinematic pair that the main flexion movement of the knee that we rehabilitate after knee arthroscopy or knee arthroplasty is built.
The results show maximum velocity values in the X-axis of 7.3364 × 10
Figure 5 shows the result of the analysis of the positions, velocities, and accelerations of the translational kinematic pair E' of the slider connected to the linear guide. The change in position was only recorded for the X-axis, as only this coordinate is variable due to the nature of the movement of the mechanism. The analysis confirmed the design distance of the linear slider movement, i.e., approximately 0.52 m. The maximum velocity value in this case was 0.13382 m/s and the maximum acceleration was 5.3397 × 10
Knowing the results of such analyses, an actuator controller can be designed to select the appropriate CPM regime for the patient's rehabilitation needs.
In order to research to optimise the links of a CPM multibody mechanism using the Generative Design method, it is necessary to divide the mechanism into individual links, which are then optimised as separate components. The input parameters for such studies, in addition to knowledge of the geometry, are of course the values of the forces or moments and other constraints to be taken into account in the optimisation. To determine the parameters to be used for the simulation in Creo Parametric, a preliminary study of the dynamics was carried out using the Rigid Dynamics toolbox of ANSYS Workbench. Analyses included kinematic pairs A', B', C', D', and E'. They involved determining the values of the moments in each pair, in the X, Y, and Z axes, during the working movement of the mechanism in ROM.
Figure 6 shows the results of determining the values of the torques in the X, Y, and Z axes of the kinematic pair A' in ROM. Only the maximum values of these torques will be important from a Generative Design optimisation point of view. These investigations determined the following maximum values: in the X-axis, the maximum torque is 2.7042 × 10
Figure 7 shows the results of determining the values of the torques in the X, Y, and Z axes of the kinematic pair B'. These tests determined the following maximum values: in the X-axis, the maximum torque is 68.788 Nm; in the Y-axis, it is 1.0039 Nm; and in the Z-axis, it is 59.215 Nm. The maximum value of the total moment in this case is 90.691 Nm.
Figure 8 shows the results of determining the torque values in the X, Y, and Z axes of the C' kinematic pair. These tests determined the following maximum values: in the X-axis, the maximum torque is 68.117 Nm; in the Y-axis, it is 5.4788 × 10
Figure 9 shows the results of determining the values of the torques in the X, Y, and Z axes of the D' kinematic pair. Through these tests, the following maximum values were determined during the movement of the mechanism, i.e., in the X-axis, the maximum torque is 65.596 Nm; in the Y-axis, it is 54.671 Nm; and in the Z-axis, it is 7.2349 × 10
Figure 10 shows the results of determining the torque values in the X-, Y-, and Z-axes of the kinematic pair E'. Through these tests, the following maximum values were determined: in the X-axis, the maximum torque is 8.4168 × 10
The results of the torque analysis obtained in this way in each of the defined kinematic pairs are the necessary input parameters for the optimisation of the structure using the Generative Design method, with the aim of reducing the mass, assuming in the study the maximum stiffness of the links, on which the accuracy of the movements of the CPM positioner will mainly depend.
This section will present the results of the optimisation of the design of the main positioner mechanism links of the CPM device. They concern the analysis of the main links 3 and 4, which provide the main support for the rehabilitated lower limb, and the driving kinematic pair of the positioner mechanism, consisting of links 1 and 2. The choice of test materials from which new link structures were generated concerned the material used in the base structure based on commercial aluminium structural profiles, made from AL 6061. Structures were also generated using Generative Design methods made from MG-AL-ZN ALLOY and MG-AL ALLOY alloys. During preliminary research, attempts were also made to use plastics, ABS and PEEK, which due to their lower material density and stiffness could not realistically contribute to reducing the mass of the solution while maintaining an acceptable level of deformation. The first attempts to generate structures showed that the mass of the links was significantly lower in relation to the initial mass, but the deformations of the links forming the kinematic pairs studied disqualified the results obtained from the practical application. Among the other metallic materials initially selected for numerical analysis, titanium was also chosen. This material, with its very good mechanical properties, offered the hope of obtaining a generated structure which, although much denser than aluminium and its alloys, could ultimately form a high-strength, low-mass structure. In the case of titanium, the initial tests showed that the high density of the material led to a rejection of the results, as the final mass of the solution exceeded the initial mass of the positioner links. However, for the optimisation (creation of a new design) of links 1 and 2, only one material was selected—316 Stainless Steel, analogous to the basic solution of the CPM device. The results of the optimisation of each link with the Creo Parametric Generative Design tool will be presented later in this chapter.
The input parameters for the optimisation were the moment values previously determined using the Rigid Dynamics toolbox of ANSYS Workbench. The analysis looked at each of the positioner links of the CPM separately. It is not possible to create a new structure for the entire kinematic chain. The Generative Design synthesis required the additional definition of boundary conditions in the form of surfaces that had to be excluded from the optimisation, as their shape and purpose were necessary to maintain the full functionality of the original solution. In the case of link 3, these were the hinge surfaces by which the link was attached to the other moving and fixed links of the mechanism. In addition, for the purposes of the research, an additional area of 5 × 4 × 1 cm was defined in the structure of the link, which in a real solution would replace the area used to fix the support of the femoral part of the limb. An important assumption in the research was to define the plane of symmetry for the optimised solution and to identify max stiffness as a complementary parameter. Most structures cannot be generated correctly without this parameter. Results were generated assuming a volume limit of between 20% and 50%. Values below and above these assumptions did not satisfy the mass and displacement conditions of link 3 and were therefore not included in the results. For the AL 6061 material, the mass of link 3 before optimisation was 0.81712 kg. Preliminary strength tests in Creo Parametric showed that the von Mises stress for link 3 was 121.4 MPa, and displacement was 5.43 mm. Such a high value of the displacement parameter is due to the fact that the simulations have neglected the influence of the stiffness of the shaft connections 3 and 4, which in the real solution ensures sufficient stiffness of the connection in the kinematic pair 3–4. The initial results, to which we will relate the obtained results of the generated structures, will allow us to select the optimum solution in terms of minimum mass and least deformation. For each of the newly generated structures, additional numerical analyses are carried out to verify the result obtained, consisting of the determination of the strength parameters: von Mises stress and displacement. The results of the optimisation of link 3 of the positioner mechanism are summarised in Table 4, Table 5 and Table 6. The number of finite elements used in the numerical study was 23,012. A single finite element had a size of 0.003 m.
A prominent feature of the Generative Design numerical study is the mass of the optimised object and the associated output geometry that the object adopts for optimisation in Creo Parametric. This is clearly higher for the same material, as can be seen in Table 4. For the AL 6061 material, the initial mass of the link is approx. 2.64 times higher (was 2.153 kg) than the original link (0.81712 kg) in the same material. This is because when analysing and generating the new object structure, the software takes the entire volume of the object as the initial mass.
The main problem identified when attempting to use other digital engineering tools that offered the ability to perform optimisation using generative design techniques (Fusion 360 and Autodesk Inventor, among others, were used) was that it was not possible to confirm by additional strength testing that the structure under test actually met the assumed strength constraints. This was only possible by applying CAD modelling techniques that used the generated geometry to manually model a new solid object with a spatial shape similar to the optimisation result. This is a very labour-intensive and time-consuming activity when it comes to achieving quite complex spatial forms, and the end result is nevertheless an approximation of the result achieved. The Creo Parametric programme allowed such studies to be carried out without modifying the optimised shape, which is a major advantage of the tool and hence its selection.
The results of the strength analyses of the generated link 3 structures showed that the most favourable result was obtained when using AL 6061 material for optimisation at the 30% volume limit. The final object mass was 0.58 kg. Displacement was also improved by 2.48 mm compared to the original design's 5.43 mm, which in practice improved the value of this parameter by 2.1 times. The von Mises stress for the tested design was 112.74 MPa, a slight change from the initial pre-optimisation value of 121.4 MPa, with no major effect on the optimised positioner link. The accumulation of von Mises stresses and the highest value of displacement in the case studied relate to the area of the link that forms the rotational connection to links 4 and 2 of the positioner.
In the case of design tests assuming the MG-AL-ZN ALLOY material, the most favourable result was obtained for the Generative Design test at a limit volume of 50%. Although the final mass of the object was the highest of the structures generated (0.715 kg), the von Mises stress value was the lowest (86.97 MPa) and the displacement level was the lowest at only 1.66 mm. For this structure, the mass reduction was 0.10212 kg.
In the case of design tests assuming the MG-AL ALLOY material, the most favourable result was obtained for the Generative Design test at a limit volume of 40%. The final object mass was 0.5380 kg. Strength tests showed that the von Mises stress value was 99.97 MPa and the displacement was 2.336 mm. In the case of the structure generated from the material in question, the weight reduction was as high as 0.27912 kg; hence, it represented the best of the results achieved.
The same methodology was used to optimise link 4 using Generative Design techniques as was used to generate the structures for link 3. The mass of link 4 before optimisation after inflicting AL 6061 material was 0.89385 kg. Strength tests in the Creo Parametric programme showed that the von Mises stress for primary link 4 was 255.53 MPa, and displacement was 5.87 mm. The high value of displacement analogous to link 3 is due to the failure to take into account the stiffness of the shaft connecting links 3 to 4, which in a real-world solution provides adequate stiffness to the connection in kinematic pair 3–4. The above results will be the baseline to which we will refer to the results obtained from the new structures generated. The results of the optimisation of link 4 of the positioner mechanism are summarised in Table 7, Table 8 and Table 9.
The results distinguish between the generated structures by the material used. The number of finite elements used in the numerical study was 23,011. A single finite element had a size of 0.003353 m. When using the AL 6061 material, the most favourable result was obtained after optimising the Generative Design at a limit volume of 30%. The final object mass was 0.59 kg. A better displacement value was also obtained relative to the original design, as it was 4.049 mm, relative to the original 5.87 mm. The von Mises stress for the tested structure was 201.21 MPa, giving a reduction from its initial pre-optimisation value of 255.53 MPa. An even greater reduction in mass is obtained for a limit volume value of 20%, although in this case, the von Mises stress after testing was as high as 318.18 MPa, despite a similar displacement value to the optimisation at a limit volume of 30%; hence, this result was rejected. Results above the 30% volume limit were discarded due to the mass of the objects obtained, which would not translate into a reduction in the value of the actuator torques in the CPM positioner design studied.
When MG-AL-ZN ALLOY material was used to generate the structures, the most favourable result was obtained after optimisation at a limit volume of 50%. Although the mass of the object was not significantly reduced compared to the original solution, at 0.7690 kg (0.12458 kg less than the original), this solution was selected for its lowest displacement parameter value of 2.21 mm. It is worth noting that the von Mises stress values do not differ significantly when different volume limits are chosen. Thus, the factor of choosing the best solution mainly concerned the lowest mass, with a minimum displacement value.
When MG-AL ALLOY material was used to generate the structures, the most favourable result was obtained after optimisation of link 4 at a limit volume of 40%. The mass of the resulting structure was 0.5670 kg, being 0.32685 kg lower than the original mass. The displacement parameter value was 3.7318 mm, with the von Mises stress set at 202.90 MPa (originally 255.53 MPa). The result obtained at the 50% limit volume is less favourable from a mass point of view, although there is a significant improvement in the displacement parameter, which has been reduced to a value of 2.1634 mm. It can therefore be concluded that the search for an optimum solution should be limited to carrying out further retail simulations in the 40% to 50% range, where more favourable results can be obtained in terms of further mass reduction and improvement of the displacement parameter.
As with the methods described above for optimising links 3 and 4 of the CPM motion apparatus, drive links 1 and 2 were also optimised. The tool used was also the Creo Parametric software. Optimisation studies using Generative Design methods focused on the selection of a single structural material, 316 Stainless steel. Loading moments on the structure were determined in ANSYS Workbench in previous studies. The mass of link 1 before optimisation was 0.61516 kg. Strength tests in the Creo Parametric programme showed that the von Mises stress for link 1 was 0.0934 MPa, and the displacement magnitude was 2.8600 × 10
The most favourable optimisation result was achieved for the limit volume of 75%. The mass of the optimised link 1 was 0.452 kg, resulting in a mass reduction of 0.16316 kg. It is worth noting that the values of the displacement parameter and the von Mises stress are practically the same in the assumed boundary volume ranges from 75% to 85%. Thus, the only parameter determining the optimum solution was the mass of the object after optimisation. Below the 75% volume, the Creo Parametric software was unable to generate the optimum structure because there was not enough material to create the correct link structure.
For the Generative Design optimisation of link 2, the mass of the object before optimisation was 0.63436 kg. Strength tests in Creo Parametric software showed that the von Mises stress for link 2 was 87.9776 MPa, and the displacement magnitude was 2.8833 × 10
In the case of the link 2 optimisation study, the Creo Parametric only allowed the optimisation to be performed with a maximum volume limit of 90%. In this case, the mass of the link was reduced from 0.63436 kg to 0.538 kg (17.9% reduction). The values of the displacement parameter and the von Mises stress, due to their low value, do not affect the accuracy of the positioner movement in the practical implementation of CPM. Below the limit value, 90% of Creo Parametric was unable to generate a valid structure.
The geometric results of optimising the CPM positioner's links 3 and 4 are shown in Figure 11. The results show the geometric shape before and after optimisation using the Generative Design method.
The results obtained indicate that it is becoming necessary to change the approach to manufacturing the components (links) of the positioning mechanism. In the original CPM solution, commercially available aluminium structural profiles were used as the basic element for the mechanism. Their use required only the cutting of a specific profile to a defined length. When these profiles are replaced by structures generated by Generative Design methods, it becomes necessary to use profile casting or 3D printing techniques in the manufacturing technology. Traditional manufacturing methods could fail in this case due to the complexity of the geometry that forms the mechanism component. However, the numerical tests carried out indicate that the results obtained concerning the original solution are characterised by a lower mass and better strength parameters, i.e., the level of von Mises stress and displacement under applied moments.
Figure 12 shows the final results of the optimisation of drive members 1 and 2 of the CPM positioner and their original shapes. In the case of optimised links 1 and 2, they can be manufactured using casting techniques or a CNC machine.
The optimisation of these links slightly altered the original shape of the links, but ultimately reduced the mass of the entire positioner and significantly reduced the von Mises stress.
The simulation model was rebuilt in ANSYS Workbench to determine how the optimised motion apparatus links changed the dynamic parameters of the CPM device design. Using the Rigid Dynamics toolbox of ANSYS Workbench, a dynamics study was performed to determine how changes in the mass and shape of the positioner members affected the potential, kinetic, total, and external energy of the CPM device's positioning system. The results of the studies, in the form of a graph of the change in energy values over time for the assumed actuator motion pattern, comparing the results before and after Generative Design Optimisation (GDO), are shown in Figure 13.
From Figure 13, we can read that before GDO, the maximum value of potential energy is 286.04 J, kinetic energy is 0.20813 J, external energy is 2.8355 J, and total energy is 148.67 J. Before GDO, the minimum value of potential energy is 145.77 J, kinetic energy is 1.0507 × 10
The Rigid Dynamics toolbox ANSYS Workbench was again used to determine the effect of the GDO on the change in a total moment in the drive kinematic pair B' of the positioner. The results of these analyses are shown in Figure 14. To better illustrate the changes, they are juxtaposed for comparison with the moments obtained before optimisation, as discussed earlier and shown in Figure 7.
The comparison of moment values in the B' kinematic pair of the CPM positioning system is summarised in Table 12. Changing the latter value is the most important thing to consider from the point of view of selecting an actuator system. It is worth noting that the efforts made to optimise the positioner links of the CPM device have reduced the total moment by a value of 32.013 Nm, resulting in a reduction in the final value of approximately 35.31% of the power requirement, given the same loads on the CPM device. Such a result demonstrates the validity of the methodology used to optimise the CPM device positioner links. This allows us to significantly improve the structural performance of the designed device. It should be emphasised that the lower actuator moment is primarily a reduction in the purchase cost of the device itself, which is integrated with the mechanical gearbox to drive the positioner's motion apparatus. Typically, in order to better match the actuator range to the customer's needs, actuator distributors use the power series of the actuators they sell. Therefore, when purchasing the final solution, the achieved reduction in a maximum actuator moment represents a significant price difference. A motor that is tailor-made for the appliance will certainly translate into efficiency and reduce electricity costs during operation.
The use of Generative Design and Topology Optimisation methods for the design and development of modern medical equipment contributes to the improvement of its design parameters according to dimension–mass characteristics and the anthropometric data of patients, thus making it possible to increase its increased ergonomics and reduced energy consumption. It is worth noting that there are limitations to the use of Generative Design techniques in this study. These limitations primarily relate to the designer's restricted influence on the ultimate spatial form of the optimised object. The result obtained, despite meeting the strength conditions assumed by the designer, may not necessarily be accepted in terms of the aesthetics of the form by the consumer. It should be noted too, that the final manufacturing technology for ready-to-use optimised objects may not align with the company's preferred manufacturing technology.
ANSYS Workbench analysis of all structures of a positioning system using the Rigid Dynamics toolbox allows for indicating the position, velocity, and acceleration of all points of the mechanism. When we determine by using the values of forces and torques in the kinematics pair, we obtain complex information about the kinematics and dynamics of the mechanism. The results obtained from such analyses become the basis for conducting research using engineering tools for research using Generative Design methods. The use of modern design methodologies implemented in the CREO Parametric software makes it possible to use design generators based on artificial intelligence. In accordance with the specified boundary conditions, loads, and materials, the optimal design solution for the target cost and sustainability indicators are obtained through countless iterations.
The use of Generative Design methods to optimise the mass of the links in multibody mechanisms allows the actuator torque required to move the positioner to be reduced. In the case of this CPM solution, a reduction of one-third of the torque of the existing drive translates into a lower cost of the actuator (actuators that differ in the type series, in our case instead of ten power/price series, can be from five power/price series). The parallel reduction of the future energy consumption of the actuator is also an added value of the presented optimisation methodology using the Generative Design method. This ensures that the actuator is correctly matched to the specific application of the motion apparatus of the positioning system. In addition to a 0.86549 kg reduction in the total mass of the links, the study also considered the achievement of improved strength parameters as an added value: von Mises stress and thus lower displacement values of the optimised multibody positioner of the CPM machine. As part of future work to develop the design of the CPM device, optimising the platform to support the patient's foot based on a Delta-type parallel robot is planned. The optimisation of this part of the solution can contribute to a further reduction in the mass of the positioner and thus to a reduction in the power of the actuator that moves the whole solution.
Graph: Figure 1 View of a virtual model of CPM rehabilitation device: (
Graph: Figure 2 View of the three-dimensional virtual model of the CPM positioner using CAD/CAE analysis: (A) position of the mechanism in the bending knee phase; (B) starting position of the mechanism ready for analysis.
Graph: Figure 3 Results of the kinematics analysis of the C' kinematic pair (position, velocity, and acceleration in a range of motion) and the graphical representation of the path of movement.
Graph: Figure 4 Results of the kinematics analysis of the D' kinematic pair (position, velocity, and acceleration in a range of motion) and the graphical representation of the path of movement.
Graph: Figure 5 Results of the kinematics analysis of the E' kinematic pair (position, velocity, and acceleration in a range of motion) and the graphical representation of the path of movement.
Graph: Figure 6 Graphs of torques in the X-, Y-, and Z-axes in A' kinematics pair in a range of motion.
Graph: Figure 7 Graphs of torques in the X-, Y-, and Z-axes in B' kinematics pair in a range of motion.
Graph: Figure 8 Graphs of torques in the X-, Y-, and Z-axes in C' kinematics pair in a range of motion.
Graph: Figure 9 Graphs of torques in the X-, Y-, and Z- axes in D' kinematics pair in a range of motion.
Graph: Figure 10 Graphs of torques in the X-, Y-, and Z- axes in E' kinematics pair in a range of motion.
Graph: Figure 11 View of the three-dimensional virtual model of links 3 and 4: (A) link 3 starting shape and result after Generative Design optimisation; (B) link 4 starting shape and result after Generative Design optimisation.
Graph: Figure 12 View of the three-dimensional virtual model of links 1 and 2: (A) link 1 starting link and result after Generative Design; (B) link 2 starting link and result after Generative Design optimisation.
Graph: Figure 13 Compare the potential, kinetic, total, and external energy of the positioning system of the CPM device before and after Generative Design optimisation.
Graph: Figure 14 Compare moments in the B' kinematic pair of the positioning system of the CPM device before and after Generative Design optimisation.
Table 1 Summary of materials, masses, and loads of components of CPM device.
Detail Mass [kg] Material 1—link 1 0.61516 316 Stainless Steel 2—link 2 0.63436 316 Stainless Steel 3—link 3 0.81712 Aluminium, 6061 4—link 4 0.89385 Aluminium, 6061 5—link 5 0.61152 Stainless steel, AISI 201 6—translation system 6 0.36466 Stainless steel, 201 + Aluminium, 6061 7—thigh support + point mass 0.1455 + 24.00 Plastic, ABS 8—calf support + point mass 0.19186 + 10.70 Plastic, ABS 9—electrical linear drive 2.24429 Aluminium Alloy 10—foot support + point mass 1.2617 + 3.50 Aluminium, 6061 11—delta robot link 0.08714 Stainless steel, 201
Table 2 Material properties used in Generative Design simulation for links 3 and 4.
Parameter ALUMINIUM 6061 MG AL ALLOY MG AL ZN ALLOY Density, [kg/m3] 2710.2 1800 1800 Young's Modulus, [Pa] 6.89476 × 1010 4.61 × 1010 4.5 × 1010 Poisson's Ratio 0.3 0.357 0.305 Yield Stress, [Pa] 2.41 × 108 1.44 × 108 1.91 × 108 Shear Stiffness, [Pa] 2.65183 × 1010 1.6986 × 1010 1.72414 × 1010 Thermal Expansion, [1/K] 2.34 × 10−5 2.58 × 10−5 2.74 × 10−5 Conductivity, [W/(mK)] 180.073 73.9 78
Table 3 Material properties used in Generative Design simulation for links 1 and 2.
Parameter 316 STAINLESS STEEL Density, [kg/m3] 8000 Young's Modulus, [Pa] 2.05 × 108 Poisson's Ratio 0.28 Yield Stress, [Pa] 2.9 × 108 Shear Stiffness, [Pa] 7.37 × 1010 Thermal Expansion, [1/K] 2.34 × 10−5 Conductivity, [W/(mK)] 21.5
Table 4 Results of Generative Design optimisation of link 3—material AL 6061.
Parameter Limit Volume 20% Limit Volume 30% Limit Volume 40% Limit Volume 50% Starting mass, [kg] 2.153 Valid value, [%] 14.9 26.9 38.3 50.2 Parameters of link 3 after Generative Design optimisation Displacement, [mm] 6.038 2.48 1.7284 1.0884 Von Mises Stress, [MPa] 279.76 112.74 101.01 87.06 Final mass, [kg] 0.3210 0.5800 0.8240 1.0800
Table 5 Results of Generative Design optimisation of link 3—material MG-AL-ZN ALLOY.
Parameter Limit Volume 20% Limit Volume 30% Limit Volume 40% Limit Volume 50% Starting mass, [kg] 1.43 Valid value, [%] Not generated 26.4 38.1 50.0 Parameters of link 3 after Generative Design optimisation Displacement, [mm] - 4.27 2.63 1.66 Von Misses Stress, [MPa] - 100.83 100.94 86.97 Final mass, [kg] - 0.3770 0.5440 0.7150
Table 6 Results of Generative Design optimisation of link 3—material MG-AL ALLOY.
Parameter Limit Volume 20% Limit Volume 30% Limit Volume 40% Limit Volume 50% Starting mass, [kg] 1.43 Valid value, [%] 15 27 37.6 50.0 Parameters of link 3 after Generative Design optimisation Displacement, [mm] 7.3908 3.9095 2.336 1.662 Von Mises Stress, [MPa] 277.50 99.79 99.97 86.97 Final mass, [kg] 0.2140 0.3860 0.5380 0.7140
Table 7 Results of Generative Design optimisation of link 4—material AL 6061.
Parameter Limit Volume 20% Limit Volume 30% Limit Volume 40% Limit Volume 50% Starting mass, [kg] 2.35 Valid value, [%] 14.2 25.1 36.5 49.3 Parameters of link 4 after Generative Design optimisation Displacement, [mm] 4.0465 4.049 2.245 1.44 Von Mises Stress, [MPa] 318.18 201.21 202.60 203.03 Final mass, [kg] 0.3330 0.5900 0.8570 1.1550
Table 8 Results of Generative Design optimisation of link 4—material MG-AL-ZN ALLOY.
Parameter Limit Volume 20% Limit Volume 30% Limit Volume 40% Limit Volume 50% Starting mass, [kg] 1.561 Valid value, [%] 14.2 25.3 35.9 49.2 Parameters of link 4 after Generative Design optimisation Displacement, [mm] 4.4611 5.14 3.24 2.21 Von Mises Stress, [MPa] 240.42 201.80 202.49 202.97 Final mass, [kg] 0.2210 0.3950 0.5600 0.7690
Table 9 Results of Generative Design optimisation of link 4—material MG-AL ALLOY.
Parameter Limit Volume 20% Limit Volume 30% Limit Volume 40% Limit Volume 50% Starting mass, [kg] 1.5611 Valid value, [%] 14.2 25.1 36.3 49.3 Parameters of link 4 after Generative Design optimisation Displacement, [mm] 4.7928 6.1504 3.7318 2.1634 Von Mises Stress, [MPa] 249.96 201.12 202.90 203.02 Final mass, [kg] 0.2210 0.3910 0.5670 0.7696
Table 10 Results of Generative Design optimisation of link 1—material 316 Stainless Steel.
Parameter Limit Volume <75% Limit Volume 75% Limit Volume 80% Limit Volume 85% Starting mass, [kg] 0.61516 Valid value, [%] Not generated 74.8 78.6 83.2 Parameters of link 1 after Generative Design optimisation Displacement, [mm] - 8.3405 × 10−4 8.3404 × 10−4 8.3400 × 10−4 Von Mises Stress, [MPa] - 0.0285831 0.0285827 0.0285812 Final mass, [kg] - 0.452 0.476 0.504
Table 11 Results of Generative Design optimisation of links 2—material 316 Stainless Steel.
Parameter Limit Volume <90% Limit Volume 90% Starting mass, [kg] 0.63436 Valid value, [%] Not generated 86.2 Parameters of link 2 after Generative Design optimisation Displacement, [mm] - 1.45 × 10−3 Von Mises Stress, [MPa] - 52.3150 Final mass, [kg] - 0.538
Table 12 The comparison of moment values in B' kinematic pair of the CPM positioning system.
Moment Value before GDO [Nm] Value after GDO [Nm] 68.788 2.7136 1.0039 0.5566 59.215 58.587 Total moment 90.661 58.648
Conceptualization, R.T.; methodology, R.T. and A.Z.; software, R.T. and A.Z.; validation, R.T., P.B. and A.Z.; formal analysis, R.T. and P.B.; investigation, R.T. and P.B.; writing—original draft preparation, R.T.; writing—review and editing, R.T., P.B. and A.Z. All authors have read and agreed to the published version of the manuscript.
Not applicable.
Not applicable.
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.
The authors declare no conflict of interest.
By Roman Trochimczuk; Andriy Zdobytskyi and Piotr Borkowski
Reported by Author; Author; Author