Fabrication of precise non‐assembly mechanisms by multi‐material fused layer modeling and subsequent heat treatment

Additive manufacturing techniques offer several potentials for future design and production. One of these potentials is non‐assembly mechanisms, movable mechanisms which need no assembly after production. Especially non‐assembly mechanisms consisting of kinematic pairs face major tolerance issues. This work advances into the new field of non‐assembly mechanisms consisting of kinematic pairs from multi‐materials. The research described in this article shows how tolerance issues can be overcome by the deliberate use of intrinsic and printing‐induced shrinkage processes. Therefore, non‐assembly mechanisms produced by multi‐material printing using fused layer modeling (FLM) are heat‐treated after the printing process to reduce and adjust the joint clearance. It was found that PLA was a suitable material for this process due to its relaxation and recrystallisation behavior during heat treatment. The printing techniques and relevant shrinkage mechanisms were analyzed and explained. Furthermore, it was found that relaxation of orientations and recrystallization could be separated in two different heat treatment steps creating a possibility for “induced self‐healing.” In addition, tribological aspects of such mechanisms will be discussed.


INTRODUCTION
There are several reasons to use non-assembly mechanisms.The assembly process of conventional mechanisms produces a significant portion of the total costs of a mechanism.Therefore, non-assembly mechanisms can reduce the total costs of a mechanism.The entire omission of connecting elements enables a smaller design and further cost reduction of the non-assembly mechanism.Due to the absence of the assembly process, design provisions for assembly processes are obsolete.This enables new design opportunities for smaller and much more complex mechanisms.The recent literature review of Lussenburg et al. 1 summarizes the state of the art in the field of additively manufactured non-assembly mechanisms.Based on their classification, non-assembly mechanisms can be distinguished by different aspects.First, a categorization according to their type (compliant mechanisms or kinematic pairs) can be performed.In addition, they can be subcategorized according to the materials used.Either, a single material or multiple materials may be used for the functionality of the mechanism.Figure 1 shows this classification.
Depending on the type of non-assembly mechanisms, different challenges are faced.The major drawback of non-assembly mechanisms designed as compliant mechanisms, is the limited deflection of the mechanism.Therefore, some mechanisms, for example a crank, cannot be realized.Additionally, elastic restoring forces induced by the deflections of the mechanism often have negative effects on the systems dynamics.Furthermore, the efforts for dimensioning of compliant mechanisms-especially with large deformations-are higher than for kinematic pairs.In addition, the vulnerability to fatigue is another drawback. 2ooking at non-assembly mechanisms consisting of kinematic pairs, the surface finish of the printed bodies within a kinematic pair can be disadvantageous for a smooth movement.Furthermore, one of the major issues these mechanisms are still facing are the tight clearances required for a precise movement of the kinematic pair.The reason for this is a relatively large clearance that is mandatory between the parts of the kinematic pair in order to ensure a separation of the bodies during the additive manufacturing process.In general, there are three different possibilities where the clearances in non-assembly mechanisms consisting of kinematic pairs can be reduced-the additive manufacturing process itself, the design and the materials.
Looking at the optimization of the additive manufacturing processes itself, the clearance between both parts of the kinematic pair remains mandatory.However, if the required clearance for preventing the fusion of the bodies with a kinematic pair can be reduced to the clearance required for a precise movement (sliding clearance to transition fit) this problem can be solved.In general, this is possible since there are already additive manufacturing techniques existing that can print in such dimensions. 3However, usually the build rates of such processes are very small.For example, the build rate of Two-Photon-Polymerization (2PP) for example is at the upper end in the range of 0.001 mm 3 /s while typical build rates of the fused layer modeling (FLM) process are some mm 3 /s. 4Therefore, producing a complete non-assembly mechanism with such techniques is very time and cost intensive, and therefore, greatly limits the chance of economic success.
The work of Lussenburg et al. 1 shows that so far, several design principles have been established in order to minimize clearances and prevent the mating parts from fusing.While two works of Chen et al. 5,6 use a drum shaped joint pin, Su et al. 7 introduce a drum shaped hole.Another proposed design by Wei et al. 8 is the so-called worm shaped design with serval small circumferential contact areas.Another completely different approach is given by Calì et al. 9 They propose spherical joints where the inner body only consist out of bands produced in certain pockets of the outer body.In use, these bands are than moved out of their pockets contacting the outer body.Li et al. 10 propose something similar.Instead of using bands the use spherical nobs on the inner body so called markers produced in dents in the outer body.Nevertheless, the dents-only required for production-remain.This limits the usable deflection of the joint so that the problem remains at least partially.However, all of these techniques always reduce the contact area within the joint.This leads to higher contact pressures within the joints compared to joints with a complete contact area, and therefore, most likely leads to increased wear.
To fully exploit the potential of additively manufactured non-assembly mechanisms consisting of kinematic pairs for more sophisticated applications in industrial context, neither significantly increased costs nor increased wear, larger dimensions or limited travel are acceptable.Therefore, keeping the contact area as large as possible as well as eliminating design provisions like dents at a low manufacturing effort must be the goal.A promising approach is given by Anghel et al. 11 They used an artificial neural network to optimize the print settings in order to optimize the minimal clearance of a cinematic pair.Only few efforts have been undertaken to reduce the clearance by means of material optimization in the past. 1 Lussenburg et al. 1 identified the field of non-assembly mechanisms consisting of kinematic pairs and multiple materials as a blank so far.Looking at new possibilities for non-assembly mechanisms with a multi-material approach, using different shrinkage behaviors of various materials is promising.It is known that in the FLM process specifically adjusted printing parameters and materials can suppress crystallization processes and freeze internal stresses as well as molecular orientations introduced during printing.By applying a heat treatment, these suppressed processes can relax, and therefore, generate changes in shape and dimensions of the part.These techniques-also known as 4D-printing-have been investigated for different materials including PLA, different printing technologies and used for several purposes.Chalissery et al. 12 for example, used a poly(ether urethane) to print hands-free door openers and shrink them afterwards onto a door handle by applying heat.Bodaghi et al. 13 as well as Hu et al. 14 made efforts towards simulation of the dimensional change of FLM printed self-bending structures.Based on similar principles Van Manen et al. 15 showed that even complex self-bending structures can be achieved.The work of Rajkumar et al. 16 and Zhang et al. 17 made deeper investigations about the underlying mechanisms especially for polylactic acid, high-impact polystyrene and acrylonitrile-butadiene-styrene.The recent review about 4D printing of Khalid et al. 18 gives a good summary how the 4D printing techniques are used.However, it also shows that these techniques have barely been used to optimize non-assembly mechanisms so far.Only one master thesis from Seoul National University was found that reduced the clearance of a non-assembly rolling contact joint by means of multi-material 4D printing. 19In this approach a connecting element in form of a thin sheet was printed from PLA in-between the two rolling bodies.After printing, the mechanism was heat-treated resulting in contraction of PLA bringing both rolling bodies closer together.The resulting mechanism can be classified as compliant mechanism from multiple materials due to its two not interlocking rolling bodies and the solid connection between both bodies.
For this work, a different approach was chosen.In order to be able to use 4D printing techniques to reduce the clearance in non-assembly mechanisms consisting of kinematic pairs, materials with different contraction behavior need to be used for the different bodies.During a heat treatment one material contracts while the other has no significant dimensional change.The benefit of such a technique is that the contact areas within the joints are not reduced and the deflections of the joints are not limited by design provisions.Nevertheless, the production time and costs will be increased but not to the same extend as for more precise additive manufacturing techniques.
Therefore, the presented work gives a new material-based approach by using the differences of specific material properties in multi-material printing of kinematic pairs.The goal of this work is to reduce the clearances of kinematic pairs (revolute joint) to an accurate fit required for a plain bearing.To achieve this, the FLM process combined with an additional heat-treatment post-process was chosen (see Figure 2).The basic principle how such non-assembly mechanisms can be produced and the underlaying material aspects are discussed.

Materials
As

Specimens: Preparation, heat treatment and geometry
All parts were printed with an Ultimaker S3 by Ultimaker BV without any enclosure.Both hot-ends were equipped with a standard nozzle type AA with 0.4 mm in diameter.A standard glass build plate was used and coated with DIMAFIX from Dima3D bevor each print.The preparation of the printing files was done with CURA 4.8.0 form Ultimaker BV.For each material, printing parameters were established and kept constant for all printed specimens.Table 2 shows the main parameters, the right side of Figure 3 illustrates the printing strategy.The heat treatment of the printed non-assembly mechanisms was performed in a universal oven UFE 400 from Memmert GmbH & Co. KG.The samples were placed in the oven at room temperature and heated afterwards.A heating rate of approximately 2 K/min was chosen in order to let the relatively large specimen follow the oven temperature to 70 • C-slightly above the glass transition temperature.This heat treatment temperature was kept constant for 4 h.Afterwards, the samples were slowly cooled down to room temperature.To ensure a constant cooling rate over the whole cooling cycle, the time to reach room temperature was set to 250 min.For all material investigations, cubes with a nominal edge length of 7 mm were printed with the parameters presented above.The true dimensions after printing were within ±2% of the nominal value.The printing orientations-X-and Y-orientation within the printing plane, Z-orientation in vertical direction-were marked on each sample.For dynamic scanning calorimetry (DSC), these cubes were subdivided into 27 smaller sub-cubes.These were labeled according to their position in X-, Y-, and Z-direction.The right side of Figure 3 shows the labeling indices.
In this work, the non-assembly mechanisms were produced by shrinking the outer body (PLA) of the kinematic pair during the heat treatment process while the inner body (ASA/i150) did not undergo significant changes in dimensions.Generic revolute joints designed as non-assembly mechanisms consisting of kinematic pairs have been used, since revolute joints are frequently used in several mechanisms.Figure 4 shows the geometry used for this study.The dimensions   of the inner part were kept constant.The inner diameter on top and bottom of the revolute joint was set to 8 mm.An empiric approach was chosen in order to adjust the clearance of these joints.Therefore, the circumferential design clearance before printing was reduced stepwise by 0.1 mm from 0.7 to 0.4 mm by adapting the outer body.Three specimens for each material combination and design clearance were produced resulting in a total of 24.To investigate if the results can be transferred to complex mechanisms, a Watt's linkage containing the non-assembly revolute joints was produced and evaluated.

Torque and clearance measurements
On the left side of Figure 5, a sketch of the experimental setup for torque measurements is shown.A bracket (A) is installed on a rotating table (B).The specimen (C) is clamped with one end into the bracket so that the rotational axis of the specimen lines up with the rotational axis of the rotating table without touching it.The other end of the specimen is placed between two pins of the torque arm (D) which is installed on a force transducer (E) rated at 200 N.This setup compensates minor misalignments and allows to only measure the force caused by the frictional torque.The experiment is performed on specimens after heat treatment which have not been actuated before the measurement.The installation of the specimens in the test setup is done in the initial position indicated with 1.The actuation of the specimens is done in four sequences with a target velocity of 3 rev/min.Due to the frictional torque the resulting velocity is lower.In the first sequence, the rotating table is rotated clockwise by 0.3 revolutions to position 2 causing an actuation angle  of −108 • .The second sequence rotates counterclockwise back to position 1 ( = 0 • ).Sequence three and four are following analog in the other direction between position 1 and 3 ( = 108 • ).This cycle of sequences is than repeated 20 times.During the whole time the force and the position of the rotating table is measured with a data acquisition rate of 100 Hz.From the measured force, the frictional torque can be calculated with the lever between the rotational axis and the contact point of the torque arm (11.50 mm).The position information is measured at the motor of the rotating table .Since the specimen has a limited stiffness, a clearance between the specimen and the contact points of the torque arms exists and the rotating table is driven by the motor via a tooth belt, the position information is not precise and can only be evaluated semi-quantitatively.
After the torque measurements, the clearances of the same non-assembly joint specimens were measured.A test setup similar to a tensile test was used.A sketch of the test setup is shown on the right side in Figure 5.The upper part of the test rig consists of a computer driven movable load frame with a position sensor and is equipped with a force transducer (E) rated at 200 N, a pack of leaf springs (suspension) (F) and the upper mounting bracket (G) for specimen.The force transducer is directly mounted to the load frame.Between the force transducer and the upper mounting bracket, the suspension is installed.This suspension allows a lager movement of the load frame without applying high tensile stresses to the specimen.The lower part of the test rig consists of the lower mounting bracket (H) for the specimen.A rigid frame connects the upper and the lower part.The specimen (C) is clamped into the mounting brackets.The force introduced by this clamping is then relieved by moving the load frame accordingly.This position is set as zero displacement.The specimen is alternately tensile and compression loaded.The loading of the specimen is performed position controlled with a constant speed of 0.05 mm/s.The displacement amplitude is set to 0.15 mm in each direction resulting in a load not exceeding 20 N to prevent the joint form being overloaded.Each loading cycle (compression/tension) is performed twice.
For evaluating the joint clearance, the force is plotted over the displacement.Figure 6 explains the evaluation method.A rigid part with no clearance causes the suspension to flex, and therefore, generates a force linearly dependent on the F I G U R E 6 Sketch showing the evaluation method of clearances.displacement (green), which characterizes the stiffness of the linear elastic system.If an assembly with a clearance is undergoing the change in loading direction-from compression to tensile loading-theoretically the counter parts do not contact each other for a certain distance.Therefore, no load transfer takes place while the clearance is overcome.Before and after this phase the load is transferred causing suspension and bulk materials to flex (red).Effects like for example misalignments or small nonlinear elastic deformations lead to an apparently lager clearance and causing a hysteresis to occur, since loading and unloading causes different slipping, and therefore, loading behaviors (blue).The clearance was defined as the displacement between both ends of the linear segments.

Dynamic scanning calorimetry
To characterize the materials, dynamic scanning calorimetric measurements under nitrogen atmosphere were performed with a dynamic scanning calorimeter (DSC) Polyma 214 from Netzsch Gerätebau GmbH.An amount between 9.0 and 10.3 mg of the filaments was prepared into aluminum crucibles with a pierced lid.The samples were measured according to the procedures presented in Table 3.The heating rate was set to 5 K/min in order to be able to separate recrystallisation and melting effects.The first heating cycle was performed to eliminate effects from previous processing steps, as well as ensure good contact to the crucible.From the following cooling cycle, the crystallization temperature was determined.The next heating cycle was used for the determination of the glass transition temperature, recrystallisation temperature as well as melting temperature.
To determine the state of the printed PLA before and after the heat treatment only the first two segments of the DSC program for PLA were performed on sub-cubes (refer Figure 3).For these measurements the sample mass was between 10.2 and 14.5 mg.

Dilatation measurements
To investigate the dilatation of the materials during the heat treatment, thermomechanical analysis was performed with a thermomechanical analyzer (TMA) TMA 402 from Netzsch Gerätebau GmbH.A dilatation probe with a spherical tip of 3.3 mm diameter was used.A constant load of 19 mN was applied to the dilation probe to ensure proper contact between probe and specimen while keeping load-induced creep effects as small as possible.Different samples of each material were measured in each direction (x-y-z).Before each measurement the dimension of the designated orientation of the sample was measured using a micrometer.The thermomechanical analysis was performed with two different temperature programs shown in Table 4.To investigate the material behavior as close as possible to the conditions in the universal oven, the heating and cooling rates were set according to the heat treatment performed in the oven to 2 and 0.2 K/min.Program 1 was used for quantitative characterization of the material behavior during heat-treatment.Therefore, multiple measurements for each direction were performed.Eight tests of each material in each direction were realized.The tests were blocked by material and orientation.For statistical evaluations a point at the end of the isothermal segment (265 min) was chosen.Program 2 was used to qualitatively investigate behavior at higher temperatures.Only one measurement per direction was performed so far.

Statistics
Statistical analyses were performed.For this analysis the arithmetic mean value as well as the confidence interval ci  for a level of significance  (or probability of an -error) of 0.05 were calculated.This calculation was done according to DIN 1319-3:1995-01. 20The reason for choosing the confidence interval is that it considers the amount of experiments performed and gives a more reliable value for the deviation compared to a pure standard deviation or standard error.A two-sample t-test 21 (valid for same variances of the samples) was used.A significance level  of 0.05 was chosen.Since the p-value is widely known, it was calculated as the two-sided probability quantile p of Gossets probability distribution. 22owever, it adds no further information, to the t-test.

Orientation relaxation
There are two relevant effects when considering orientation relaxation that will be discussed.It is known that dependent on the thermal energy in the polymer, the molecules can perform micro-or macro-Brownian movements. 23In a molten polymer, complete molecular chains perform free movements known as macro-Brownian movements.Once the melt solidifies, the macro-Brownian movements are suppressed.In this state, the polymer chains are unable to slide against each other (without applying external forces/energy).However, segments of the polymer chains are still able to perform movements.These are known as micro-Brownian movements.Below a certain thermal energy level, related to the glass transition temperature, these movements are suppressed and the polymer chains are frozen. 23Macro-and micro-Brownian movements of polymer chains lead to an irregular arrangement and thus entanglements of the chains within the material.Therefore, within a resting melt, the molecular orientations are in a state of equilibrium.In general, higher thermal energy levels lead to quicker movements of the polymer chains.
An opposite effect can be obtained once a melt is sheared.A velocity profile establishes within the melt, and therefore, tends to orientate the polymer chains in the direction of the velocity vector or rather the flow direction.In general, higher velocities lead to stronger orientations and longer polymer chains tend to disentangle slower when sheared.
Within a sheared melt, macro-Brownian movements as well as orientation processes take place at the same time.The Brownian movements lead to relaxation of the introduced orientations over time.If the orientation process is faster than the relaxation process, the molecules get orientated in the polymer melt.Once shearing is stopped, orientation processes no longer take place but Brownian movements still remain as long as the temperature is above the glass transition temperature.Therefore, the orientations within the polymer will be relaxed successively over time. 24The required time for this process is called relaxation time, which sensitively depends on temperature.
Figure 7 shows a schematic sketch of the situation in the FLM-process.During the FLM-process the polymer melt is significantly sheared.Depending on material and printing parameters, the polymer melts can be sufficiently sheared to orientate the molecules during printing causing a shear-thinning behavior of the melt.First, the polymer melt is sheared through the nozzle.To calculate the shear-profile within the nozzle the following equations can be combined.The viscosity  is defined as the proportionality factor between the shear stress  and the shear rate ̇ (Formula (1)).The Hagen-Poiseuille equation for Newtonian flow in cylindrical capillaries with a diameter of 2 * r and a length L is shown in Formula (2).It allows to calculate the volume flow rate Q from the pressure difference ΔP over the length L and the viscosity.To consider the non-Newtonian behavior of a polymer melt, the Weißenberg-Rabinowitsch correction given in Formula (3) can be used.From this equation the Weißenberg-Rabinowitsch corrected shear rate ̇corr can be calculated with the exponent of the power law regime m of a shear-thinning material.Combining the Formulas (1), ( 2) and ( 3) with the definition for the shear stress  and the geometic dimensions of the cylindrical capillary leads to Formula (4).The idealized volume flow rate can be calculated from the line width w l , print speed v p and layer height h l according to Formula (5).
F I G U R E 7 Melt behavior during FLM-printing; colors of arrows: red-heating, blue-cooling, black-melt velocity, gray-melt flow and printing direction.
Behind the nozzle outlet, the upper part of the strand moves with the velocity of the nozzle, while the lower part is fixed at the lower surface, leading to velocity gradient.In this region, the shear rate can be estimated as the ration of print speed v p and layer height h l as shown in Formula (6).
Directly behind the nozzle, the melt it is cooled down.Introducing a high cooling rate behind the nozzle reduces the time to reach glass transition temperature to be shorter than the relaxation time for some polymers.In this case, molecular orientations are frozen within the printed parts.
These frozen orientations in the part can still relax afterwards.By heating the part above glass transition temperature, micro-Brownian movements occur.Since they allow sufficient movement of the molecular chains, the relaxation of the frozen molecular orientations can take place in a solid state.This so-called orientation relaxation again leads to a contraction in the direction of orientation (=former direction of motion) and a transversal expansion.The contracting effect can be used to shrink the outer body of a kinematic pair onto the inner body and reduce the clearance in a non-assembly mechanism consisting of kinematic pairs.

Recrystallization
It is well known that depending on the chemical structure, a thermoplastic polymer can either be amorphous or semi-crystalline.For semi-crystalline polymers, the chain mobility-which depends on temperature, chemical structure as well as length of the polymer chains-defines the crystallization speed, and therefore, the time to complete formation of the crystals.This means in general the crystallization of all semi-crystalline polymers can be more or less suppressed depending on the cooling rate.In industrial processes polymer melts are usually cooled down rapidly.However, many polymers still exhibit sufficiently high crystallization speeds to gain crystallinity.Nevertheless, in certain cases crystallization is deliberately suppressed by quenching during processing, in order to achieve certain properties like transparency or low shrinkage.Polyethylene Terephthalate (PET) used in beverage bottles, stretch wrapping films and polymer fibers are probably the most common examples for this effect.Whenever crystallization was suppressed during processing, the molecules are not in their thermodynamical equilibrium state.By adding sufficient thermal energy to allow micro-Brownian molecular movements within the polymer, the molecules will start to reorganize and form crystals.This recrystallization process takes place above the glass transition temperature and below the melting of the crystals.Therefore, recrystallisation takes place in a solid state also known as cold crystallization.When crystallites are formed, the volume decreases for most polymers since the crystallites have a higher density than the amorphous polymer structure.This volume decrease obviously leads to a dimensional reduction in all directions and thus can be used for the described production process of non-assembly mechanisms.

Single revolute joint
The actual printing time of a single revolute joint with a volume of ca.1460 mm 3 was roughly 100 min.This result in an average build rate of ca.0.24 mm 3 /s which is a rather slow pace for FLM due do the chosen parameters and the multi-material printing.Afterwards 8 h of heat treatment is added for adjusting the clearance of the non-assembly mechanism.Considering some additional efforts, like removing the part from the build plate etc. the total production time of such a revolute joint is about 10 h.Comparing this to a micro additive manufacturing technique like for example Two-Photon-Polymerization (2PP) a significant difference can be observed.Looking at the data of Hanh et al. 4 the build rate of 2PP is at the upper end in the range of 0.001 mm 3 /s.With this build rate printing, the revolute joint with the 2PP process would take roughly 400 h.Even if the build rate was 10 times as high, the printing of the joint with 2PP would take four times as long compared to the presented process using FLM and heat treatment.Besides our described process being the comparably cheap, this clearly shows one potential of our new method.
After printing and heat-treatment, the revolute joints were tested regarding their frictional torque within the first 20 cycles.Figure 8 shows the frictional torque in dependence on the actuation angle  of an ASA/PLA joint with 0.6 mm clearance.For the first cycle, the sequences are marked separately for better understanding.The arrows indicate the rotational direction of the sequences or rather the evolution of the torque over angle and time during a sequence.In the first sequence of the first cycle a small rotation without any torque, followed by a nearly linear progression of the torque up to approximately  = −20 • can be observed.The torque-free rotation is related to the clearance between specimen and the pins of the torque arm followed by an elastic bending deformation of the joint causing the nearly linear progression.Afterwards the curve proceeds nonlinearly but overall increasing to a maximum close to  = −90 • .This kind of progression with a maximum around || = 90 • could indicate an ovality of the joint.Since in the second sequence the revolute joint now moves in the opposite direction, first the remaining torque of the previous sequence is released, followed by a rotation without causing any torque due to the described clearance in the setup.Afterwards, the torque quickly increases to its maximum followed by a reduction to its minimum at the initial position ( = 0 • ).This minimum can be explained by the fact that the joints were heat-treated in this position.Due to the softening during heat treatment-especially of PLA-the faces are properly mated in this position.The sequences three and four are analog to the previous sequences but in reverse rotational direction, causing a change in the sign of angle and measured torque.Due to the relatively high maximum torque in the first sequence of the first cycle for combinations of ASA and PLA three revolute joints broke (one of each design clearance except for 0.7 mm).For the remaining joints, it was found that the qualitative behavior of the joint does not change with increasing number of cycles.However, the frictional torque decreases with increasing number of cycles.
Similar observations as for ASA-PLA non-assembly mechanism revolute joints could be made for combinations of i150-PLA.Figure 9 shows the frictional torque in dependence on the actuation angle  of an i150-PLA joint with 0.6 mm clearance.Again, the minimal torque is found in the region of  = 0 • .Except for the first sequence of the first cycle, the torque value range is much more constant over the actuation angle with periodically occurring sharp peaks within the baseline.This could indicate a rounder geometry of these joints.The sharp peaks within the progression of the segments in the first and second cycles indicate stick-slip effects.However, the joint is running in over the first two cycles, leading to a rapid decrease of the jerky movement which can be explained by the formation of a thin PTFE transfer film 25 -from the PTFE particles incorporated in i150-between the mating surfaces which need some motion cycles to evolve.Like the other material combination, the frictional torque of joints from i150-PLA decreases with increasing amount of cycles.For this material combination, one joint (0.7 mm design clearance) failed due to overloading.
Figure 10 summarizes the decrease in torque over the number of cycles.It exemplarily shows the maximum torque T of each sequence in dependence on the cycle for an i150-PLA joint with 0.6 mm design clearance.For all investigated joints, a quick decay within the first two to three cycles was observed asymptotically proceeding towards a constant value for larger amounts of cycles.The explanation lies in the running in wear behavior.During each cycle, wear occurs causing  the contacting faces to adapt to each other and reducing contact pressure.The reduction of contact pressure then leads to a reduction in wear and so on.
Combining this information form all tested joints leads to Figure 11.The average of the maximum torque of sequence 3 for ASA-PLA and i150-PLA joints for the first and the 20th cycle is plotted over the design clearance.The previously explained decay of torque between the first and the 20th cycle can be clearly seen.In addition, a tendency concerning the design clearances can be observed: The larger the clearance the smaller the average maximum torque.This fulfills the expectations, since a lager clearance before printing leads to a smaller contact pressure after heat treatment, and therefore,-implying a constant force independent coefficient of friction-to a lower resulting frictional torque.Even though a more constant torque distribution was observed for combinations from i150 and PLA, no significant reduction in average maximum torque due to the usage of i150 could be observed.This nicely shows that a more specific optimization of the material combination within the non-assembly mechanism joints is mandatory to further improve the tribological performance.
Figure 12 exemplarily show the evaluation of the clearance after heat treatment and 20 actuation cycles.In Figure 12, the data of a non-assembly revolute joint from ASA and PLA after 20 actuation cycles with a design clearance of 0.4 mm at a  = −90 • position is shown.As described in Section 3, the difference between odd (pulling) and even (pushing) is related to the joint clearance.
Figure 13 shows the results of the clearance evaluation for ASA-PLA joints.On the one hand, it was found that for nearly all joints in the  = 0 • position-the position during heat-treatment-the clearance is not detectable.The same explanation as for the minimum torque in this position can be given.Due to the softening during heat treatment, the faces are properly mated in this position reducing the clearance to its minimum.In comparison to that with some exceptions the positions  = −90 • and  = 90 • show a significant clearance.This is another indication for the ovality of joint from ASA and PLA.In addition, for the positions  = −90 • and  = 90 • an expected decrease in clearance after heat treatment with decreasing design clearance was found.For joints from i150 and PLA, no clearance could be measured for any joint in any position.On the one hand this means, that there is no-or at least no measurable-ovality.On the other hand, since the design as well as the shrinking material was kept constant it means that the i150 must have significantly different behavior during printing and heat treatment.

F I G U R E 13
Clearance after heat treatment and 20 actuation cycles of non-assembly revolute joints from ASA-PLA.

Material aspects of PLA
To analyze the material state before and after heat treatment, DSC-measurements from three samples diagonally trough an untreated PLA cube printed with 60 μm layer height were performed.The curve progression of samples diagonal through a single cube are similar.Figure 14 shows the result of these DSC measurements.Before the heat-treatment was performed, the absolute values of the recrystallisation enthalpy and the meting enthalpy are found to be both at 27 J/g.This indicates that the untreated specimen is amorphous throughout the complete cross section.In contrast to that after the heat treatment at 70 • C the recrystallisation enthalpy was reduced to 20 J/g indicating a minor recrystallisation.Nevertheless, the specimen is still mostly amorphous.After a heat-treatment at 70 • C followed by a heat-treatment at 80 • C, the specimen shown no recrystallisation anymore.Therefore, most of the recrystallisation takes place during the 80 • C period and where the specimen reaches its maximal crystallinity.Since the heat-treatment was performed at 70 • C, significantly lower than the beginning of the recrystallisation (between 85 and 90 • C), no recrystallization should take place.The dilatation behavior of highly oriented printed PLA cubes during heat-treatment is shown in Figure 15.Measured curves closest to the calculated arithmetic mean of their group at the end of the isothermal segment are displayed.The curves for all directions reach a constant value 4 h into F I G U R E 14 DSC measurements (first heating cycles) of a diagonal trough PLA cube printed with 60 μm after different thermal treatments.

F I G U R E 15
Selected TMA measurements in X-Y-Z-direction of PLA cubes printed with 60 μm while heat-treatment at 70 • C; arithmetic mean and confidence interval at end of isothermal segment indicated.the isothermal segment.In X-and Y-direction the results show a contraction of approximately 4% after the heat treatment without significant differences between both directions.A p-value of ca.0.91 was obtained from the two-sample t-test.The similarity between X-and Y-direction was expected since there should be no difference in shearing or cooling within X-and Y-direction due to the chosen printing strategy (refer Figure 3).Opposing to that, the Z-direction shows an expansion of approximately 8.5% caused by orientation relaxation.Recrystallisation typically leads to shrinkage, and therefore, has no dominant role.The slight decrease of the curve for Z-direction indicates an ongoing recrystallisation processes, which takes place simultaneously to the orientation relaxation but at a slower pace.This can be explained as follows.The heat treatment temperature is above the glass transition temperature of the investigated material.Therefore, micro-Brownian movements occur in the material.Considering that, relaxation of orientations to a random coil in the amorphous segments requires less chain movements compared to formation of highly ordered structures in crystallites, molecular orientations can be relaxed while recrystallisation only takes place to little extend.
From the previous observations, we can anticipate that the additional heat-treatment at higher temperatures will complete the recrystallisation process without any further orientation relaxation.The results which confirm the previous assumption are shown in Figure 16.It can be seen that for all three directions X, Y and Z with the starting of heating to 80 • C, a small thermal expansion occurs followed by an asymptotical decrease in dimension.Considering that this shrinkage is underestimated since roughly 25% were already recrystallized during the 70 • C period, it is less than 1%.This is only a quarter compared to the shrinkage in X-and Y-direction caused by orientation relaxation.Since a sufficient clearance is mandatory for printing-at least for small geometries-the pure shrinkage due to recrystallisation of this specific PLA seems to be insufficient to adjust the clearance in non-assembly mechanisms in the first place.However, since both processes can be separated-at least to a major portion-it will be possible to use this effect at a later point in the lifecycle of non-assembly mechanisms as a kind of "induced self-healing feature."After a certain amount of wear occurred in the mechanism, the remaining crystallization potential can be used in a second heat-treatment at 80 • C to force recrystallization.The shrinkage induced by this triggered recrystallisation is than used to compensate the wear induced clearance.This recently applied pending patent 26 opens completely new possibilities for expanding the lifetime of such mechanism, and therefore, making it more sustainable.
The previous results proved that the relaxation of molecular orientations is the main effect for shrinkage.As discussed in Section 3.1, the orientations are introduced during printing by extruding the material trough the nozzle as well as moving the printhead over the melt strand.Considering that the amount of orientations is dependent on the shear velocity and the amount of frozen orientations is related to the shrinkage a dependence of the shrinkage on the share rate during printing is implied.Referring to Formulas (4) and ( 5), it can be seen that the shear rate, and therefore, the amount of introduced orientations while extrusion through the nozzle depend on the nozzle diameter, the line width, printing velocity and layer height.In comparison to that, the shearing due to the passing of the nozzle over the deposited melt stand is only dependent on the printing velocity and layer height (Formula ( 6)).Furthermore, for both shearing regions the shear rate is proportional to the printing velocity.Opposing to that, inside the nozzle the shear rate is proportional to the layer height while after the nozzle the shear rate is inversely proportional to the layer height.
This inverse proportionality of the shear rate to the layer height in der different regions allows us to identify which region is the most relevant for shearing the material.Therefore, all parameters where kept constant and only the layer height was varied.The results of these experiments are shown in Figure 17.TMA measurements in Z-direction of PLA cubes printed with 60, 100, and 150 μm while heat-treatment at 70 • C are shown.It can be clearly seen that the expansion in Z-direction decreases with increasing layer height.Therefore, the amount of frozen orientations is inversely proportional to the layer height.From this observation, we can conclude that the shearing of the melt after exiting the nozzle is the relevant mechanism for orienting the polymer chains.Calculating the apparent shear rate (without considering the non-Newtonian behavior) in both regions comes to the same result (refer Table 5).Since the shear rates inside the nozzle are in a very low range, molecular orientation is rather improbable.This leads to the conclusion that for controlling the material shrinkage during heat-treatment the relevant parameters during processing are layer height and printing velocity (compare Formula (6)).Furthermore, the printing temperature as well as the cooling speed are crucial parameters when deliberately freezing molecular orientations.

Material aspects of i150 and ASA
To complete the material investigations also the behavior of the "static" materials i150 and ASA during the process was investigated.In Figure 18, the dilatation behavior of i150 is shown.Similar to PLA, a contraction in X-and Y-and an expansion in Z-direction can be found, indicating frozen orientations after printing.The most important difference between i150 and PLA is that in X-and Y-direction a contraction of approximately 1% can be observed-in Z-direction an expansion of approximately 1.7%.Since the PETG matrix of the i150 is unable to form crystallites the effect must be entirely related to orientation relaxation.Furthermore, it is clearly visible that the orientation relaxation is not finished at the end of the isothermal segment since no constant value is reached.This indicates a longer relaxation time which can be explained by lower molecular mobility compared to PLA.The glass transition-related to freezing of micro-Brownian molecular movements-of the PETG matrix of i150 is in the range of the heat-treatment temperature only allowing a small amount of micro-Brownian molecular movements.
Figure 19 shows the dilatation behavior of ASA cubes printed with 60 μm during the heat treatment with 70 • C. For Xand Y-direction, an expansion during heating followed by an asymptotic decay in dilation during the isothermal segment of approx.0.1% was found.Looking at the dilation value after cooling, it can be seen that this value is negative.This implies that the effect during the isothermal segment is irreversible.The absolute value of this reduction (ca.6 μm) is so small that creep effects during the measurement at 70 • C could be a significant portion.It could not be clearly identified if this effect is related to reorganization of molecules within the material.However, this seems rather improbable since the heat-treatment temperature is about 30 K below the glass transition temperature of ASA.Same as for X-and Y-direction, the Z-direction shows a small decay of ca.0.01% (ca. 1 μm) during the isothermal segment.This is most likely related to creep effects.Furthermore, the dilatation value after cooling remains positive.Therefore, an irreversible portion of the dilatation is present.In combination with the effects found for X-and Y-direction this could be an indication for orientation relaxation processes to occur even though the heat treatment temperature is well below the glass transition temperature.However, to be sure a deeper investigation is required.

Watt's linkage
With the previous results, it was investigated if the concept of the non-assembly revolute joints can be transferred to more complex mechanism like a Watt's linkage.For this purpose, a Watt's linkage containing four of the previously developed revolute joints was used.The frame and the inner link were made from i150/ASA, the outer links of PLA. Figure 20 shows a sketch of the non-assembly Watt's linkage and its movement during heat-treatment.Since the outer links are made of PLA, they contract over their whole length, and therefore, change the distances between the rotation axis of frame and inner link.This also causes a rotation of the inner link.To achieve the desired motion of the Watt's linkage after heat-treatment, the length of each link needs to be accurate.To achieve this-based on the previously investigated shrinking behavior-the length of the outer links was increased to compensate the shrinkage.Nevertheless, there is a downside to this design.The first problem might be that due to an asymmetrical shrinkage of the outer links a translatory motion of the inner link can occur.Furthermore, the previous results have shown that PLA is amorphous before heat-treatment.Around the glass transition of an amorphous polymer, the stiffness significantly decreases.As discussed before, the heat-treatment (70 • C) is performed at temperatures above the glass transition of PLA (onset: 56 • C) to initiate the shrinking process.The rotation of the inner link during heat treatment obviously causes a rotation in the joints between inner and outer linkages.Due to friction in the joint, it creates a bending moment onto the rods of the outer links.The left image of Figure 21 shows the result of this effect on a non-assembly Watt's linkage of PLA and ASA.The remaining stiffness of PLA is insufficient to prevent plastic deformation of the outer linkages.The ASA components are not affected since the heat-treatment temperature is well below the glass transition temperature (onset: 97 • C).
To overcome this problem the design of the outer linkages was adapted.The rods of the outer links were designed with the same material as the frame and inner link.This gives the rod more stiffness at heat treatment temperature.The connection between both materials was spliced in order to improve the strength of the connection.The right image of Figure 21 shows the results of this design change on a Watt's linkage from PLA and i150.Even though the glass transition of i150 (73 • C) is only shortly above the heat treatment temperature, no plastic deformation can be found.Furthermore, by reducing the overall shrinkage of the link, the risk of a translational motion of the inner link is reduced.Looking at these results it seems logical to only use the shrinking materials at the faces around the joints, were shrinking is desired.

CONCLUSIONS
The presented study explores the potential of non-assembly mechanisms with kinematic pairs made from multi-materials.It was found that multi-material printing and a subsequent heat treatment can be used for adjusting the clearance of FLM-printed non-assembly mechanisms up to two times to achieve a transition fit.This second adjustment allows the implementation of a "induced self-healing feature."The proposed technique offers precise movement of nonassembly mechanisms without significantly increased cost or larger dimensions compared to traditional non-assembly mechanisms.
It was found that polylactic acid is suitable for the shrinking process due to its low polymer chain mobility.This enables suppression of orientation relaxation and crystallization by rapid cooling during printing.The layer-height and printing speed were identified as key parameters.Nevertheless, further investigations are required to precisely predict the absolute amount of shrinkage to enable a generative rather than an iterative approach for adjusting the clearance.
The proposed process route including the "induced self-healing feature" for wear compensation is shown in Figure 22.It involves adjusting the clearance of the non-assembly mechanism by means of orientation relaxation, and performing a second heat treatment triggering recrystallization processes right before unacceptable wear occurs to compensate for wear-induced clearance.This offers benefits in terms of increased lifespan for non-assembly mechanisms.
To further improve the lifespan of such non-assembly mechanisms, material combinations with pure PLA may not be suitable in terms of tribological properties.Therefore, optimized tribological material pairs are needed for polymer-polymer sliding contact to ensure longevity. 27While two materials may be sufficient to adjust the clearance, using more than two could be beneficial.A combination of a tribologically optimized, structural-mechanical

F I G U R E 2
Proposed process route for production of precise non-assembly mechanisms consisting of kinematic pairs (A) printing with clearance, (B) first heat treatment, (C) non-assembly mechanisms with precise joint clearance.

F I G U R E 3
Left: labeling indices of sub-cubes; green: 111, blue: 222, red: 333; right: printing strategy and printing orientations.

F I G U R E 4
Design of non-assembly revolute joint; materials: PLA (blue), i150/ASA (white).

F I G U R E 5
Left: setup for torque measurements; right: setup for clearance measurements.

F I G U R E 8
Torque during the first rotations of a non-assembly mechanism revolute joint from ASA and PLA with 0.6 mm design clearance; arrow: direction of sequences.

F I G U R E 9
Torque during the first rotations of a non-assembly mechanism revolute joint from i150 and PLA with 0.6 mm design clearance.F I G U R E 10 Propagation of maximum torque of each segment of a non-assembly mechanism revolute joint from i150 and PLA with 0.6 mm design clearance.

F I G U R E 11
Average maximum torque of non-assembly mechanism revolute joint from i150 as well as ASA and PLA in dependence of design clearance.F I G U R E 12 Evaluation of clearance after heat treatment and after 20 actuation cycles of a non-assembly revolute joint from ASA-PLA with a design clearance of 0.4 mm in  = −90 • position.

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I G U R E 16 Selected TMA measurements in X-Y-Z-direction of PLA cubes printed with 60 μm while heat-treatment at 70 • C followed by 80 • C.

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I G U R E 17 Selected TMA measurements in Z-direction of PLA cubes printed with 60, 100 and 150 μm while heat-treatment at 70 • C; arithmetic mean and confidence interval at end of isothermal segment indicated.

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I G U R E 18 Selected TMA measurements in X-Y-Z-direction of i150 cubes printed with 60 μm during heat-treatment at 70 • C; arithmetic mean and confidence interval at end of isothermal segment indicated.

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I G U R E 19 Selected TMA measurements in X-Y-Z-direction of ASA cubes printed with 60 μm while heat-treatment at 70 • C; arithmetic mean and confidence interval at end of isothermal segment indicated.

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I G U R E 20 Movements of non-assembly Watt's linkage during heat-treatment; before heat-treatment: light colored, after heat-treatment: full colored; dark: PLA, bright: i150 or ASA, red arrows: movements during heat-treatment.

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I G U R E 21Non-assembly Watt's linkage after heat-treatment; left: from PLA (blue) and ASA (white); right: from PLA (blue) and i150 (white) after heat-treatment.
printing materials, a Polylactic Acid (PLA) from DAS FILAMENT, an Acrylonitrile Styrene Acrylate Copolymer (ASA) from Fillamentum Manufacturing Czech s.r.o. as well as i150 from igus GmbH, a glycol modified Polyethylene Terephthalate (PETG) with embedded Polytetrafluorethylene (PTFE) particles were chosen.Relevant material properties are shown Table 1.These properties were determined by dynamic scanning calorimetry explained later in this chapter.

TA B L E 1 Relevant material properties. PLA ASA i150 PETG PTFE
Programs for DSC-measurements; hr., heating rate; cr., cooling rate.Temperature program of TMA-measurements; hr, heating rate; cr, cooling rate.

TA B L E 5
Apparent shear rate ̇a at different layer heights inside and after exiting the nozzle, line width 350 μm, print speed 20 mm/s.