# Synthesis and Numerical Analysis of Compliant Devices: A Topology Optimization Approach for Mechanisms and Robotic Systems

Authors: S. Premanand; G. Arunkumar; Venkatesa Prabhu Sundramurthy
Journal: Advances in Materials Science and Engineering
 (2022)

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## Abstract

The topology optimization design invariably shall be used in various applications such as four bar mechanisms, robotics designs, aircraft engineering designs, and many other mechanical innovative systems for improving the efficiency in the system. This research paper emphasizes more on general topology optimization design for a rectangular domain in which numerically analyzed with defined boundary conditions. Furthermore, the same setting geometry has been taken for sensitivity analysis to find the objective stress and nonstress zones. Then, the geometry is topology optimized to analyze stress, safety factor, output deflection, and mass reduction. Also this research work focuses more on topology optimization, design synthesis, and objective function comparison in different materials. Hence, the results are suitable volume and mass reduction in various robotic devices. Validation and comparison of compliance base materials will further support the paper to extend the work for experimental analysis. This final topology optimized and validated device can be manufactured and forced to experimental fatigue endurance test cycle test condition in static and dynamic state. The results outshoot the final destination of this optimization design.


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## Body

## 1. Introduction

A preprint has previously been published [1]. In the automotive and mechanism and robotics applications parts, we normally design and adapt for rigid body mechanisms to achieve greater fatigue strength and shelf life. However, recent design of engineers considered the process of reduction of excess mass in all constructive mechanisms and robotics assembly parts in order to improve vehicle efficiency without compromising the safety. In the current trend, the combinations and comparisons of various materials come into the picture during design synthesis such as rigid bodies, flexural devices, and reinforced structures with combinations of metals and nonmetals. Realization of flexible components is added in all mechanism designs of automotive and mechanism and robotic applications. Minimizing the joints and links is a challenging perspective in design synthesis for assembly components. Elastoplastic behavior design (Figure – 1.0) is chosen for mechanical motion parts design and is a trending mechanism for précised motions and accuracy.As per Shinji Nishiwaki et al., stiffness structures with allowable deformation design give better performance, hence they took optimal compliance as an objective function [2].The kinematic synthesis design is successful in applications because it has a combination of both rigid body mechanisms and compliant mechanisms composed of flexible pivots through the PRBD models developed by Kyler A. Tolman and Howell [3]. General compliant mechanism design involves mainly for mass minimization in mechanisms and robotics vehicles to improve the vehicle performance. Topology optimization methods are adopted for various components or assemblies in tedious shapes with reduced parts combined to form a single continuum part with low risk in design synthesis [4].Compliance in the joints of the robot gripper will lead to accuracy in the picking and placing of objects. Compliance in grippers will reduce the contact forces acting on them. The primary objective function of topology optimization is to maximize the stiffness by distributing material available on stress-affecting zones. The optimization techniques decide the amount of material and where it gets distributed. The primary goals to be achieved through the topology optimization are maximum stiffness with mass reduction and balancing the goals to achieve an optimal solution in part design [5].The topology optimization and its constraints to develop the part in 3D printing technologies and various methods of constraining topology optimization to obtain superior part functionality with optimum cost is the current expectations in mechanism and robotics industry. However, production vehicles require their components to be less costly with production on a large scale. The car’s performance is rated through its fuel efficiency and in which the components lesser mass is directly proportionate to that car’s performance [6].The motivation for the design of compliant devices in mechanism and robotics parts continues from previous research and success on converting compliant centrifugal clutches, compliant tweels (tyre and wheel), compliant mechanical brakes, and bicycles. In compliant mechanism designs, the continuum synthesis approach is used here for the design of distributed compliant mechanisms which is purely based on topology optimization for structures. In this method, the errors are minimized to achieve geometrical and mechanical advantages. In this, optimality criteria are based on finding suitable criteria for specialized design conditions and developing an iterative procedure to find an optimum design. Also, less objective functions are subjected to constraints and convergence is quick compared to other optimization methods [7, 8].In many situations, the reverse engineering process is carried out for the study of various mechanisms and robotics parts. For example, the car wiper parts are converted as an optimized compliant wipers through topology optimization to get an optimum compliant design. The final design enables a significant weight reduction of 20%. The weight reduction is associated with material economy, coupled with reduced energy consumption in the manufacturing stages, and as a secondary consequence, a significant reduction in fuel consumption of the car [9].The mass of the engine bracket support topology is optimally designed, which resulted in an effective lowering of the mass of the engine bracket support of nearly 20% (1243gms⟶989gms) and an NVH result of natural frequency reduction of 10% (1024 Hz⟶1122 Hz), which ultimately improved the passenger comfort [10].A compliant mechanism-based rotation pointing mechanism is designed with 2 (DOF). Compliance analysis finds the relationship between the applied load and the deflection of the mechanism and has been the focus of many researchers. [11].The motor cycle piston is taken for analysis to reduce the mass by topology optimization and maximize the stiffness by distributing material available on stress affecting zones. This is the primary objective and function of topology optimization. Topology optimization is maximum stiffness with mass reduction and balance the goals to achieve an optimal solution in parts design. SIMP (solid isotropic material with penalization) is one of the methods to achieve the maximum stiffness with proper material distribution process in material [12].Elastoplastic behavior is chosen for mechanical motion parts design, which is a trending mechanism for précise motions and accuracy. Polymers with high fatigue resistance materials like Delrin for application require many loading cycles [13]. Normality in design involves the property of a material which does not deform easily and avoids wear out in all conditions, and there is a conflict between these two attributes (flexibility and stiffness) [14].Many macro and micromanipulator designs have single-compliant crank designs with multiple degrees of freedom used in pumps and compressor applications. These parts are analyzed in FEA and design optimized to achieve compliance and accuracy in manipulator displacement [15,16]. Kinetostatic behavior should be taken into account in the design of the desired application in which the force on an elastic object causes specific displacement [17].A body is properly viewed as unyielding if the detachment between any two points in it is always constant. In reality, no body is perfectly rigid. When equal and opposite forces are applied to a body, it is always deformed slightly. Rigid bodies are bodies that cannot deform. They can translate and rotate, but they cannot change their shape. From the start, this must be unstated as a guesstimate to certainty, since not one body is flawlessly rigid. The difference between compliant mechanisms and rigid body mechanisms is compliance and elastic segmented parts with single body mechanisms or connected with pseudorigid body mechanisms (PRBMs) [18]. A flexible structure without joints and links that elastically deforms to produce a desired force or displacement.Most of the rigid body mechanisms are best suitable only for macroscale mechanisms and less suitable for microlevel scales, but the compliant mechanisms are best suitable for macro and microscale mechanisms with systems that are continuous, monolithic, and have optimum flexibility [19].Elastoplastic behavior is chosen for mechanical motion parts design, which is a trending mechanism for précised motions and accuracy. Polymers with high fatigue resistance materials like Delrin for application require many loading cycles [13], as shown in Figure 1.Figure 1
Flexural design in compliant mechanisms —for mechanisms in robotics.The automotive and aerospace parts with rigid body mechanisms are taken for analysis process based on a review of previous case studies conducted by various researchers. The development of compliant mechanisms for commercial products was started by Howell (2001) with PRBM and the parallel mechanism optimization method. Mainly, they made case studies on bicycle parallel application brakes and bicycle derailleur [13].Compliant mechanisms are a moderately new variety of single-part mechanisms which operate on flexible distortion as an action of motion. The kinematic synthesis approach explained by Frecker and Midha in emerging out for compliant mechanism fusion into rigid bodies [20]. The compliant mechanisms transmit and transform force and motion; this mainly eliminates the friction and backlash which are predominant failures in rigid bodies after continuous usage in a dynamic environment [21]. Hence, the motivation starts with adaptation of compliant mechanism designs in automotive, aerospace, and engineering support parts for reducing the part count and part weight in turn to achieve mechanical advantage and achieve precision and accuracy during motion [22].No hard and fast rule that noticed that any of the rigid bodies with many links and joints can be converted into compliant mechanism for geometric and mechanical advantage (MA). In our analysis, we chose parts with one degree and three degrees of freedom with less force action, relatively to compare we took a part with one degree of freedom plain flap in an aeroplane which has more force in action, as shown in Figure2. The mass of the engine bracket backing topology is optimally designed, which resulted in an effective lowering of the mass of engine bracket support of nearly 20% (1243gms⟶989gms) and an NVH result of natural frequency reduction of 10% (1024 Hz⟶1122 Hz), which ultimately improved the passenger comfort [23]. In this paper, a comparison between steel and aluminium applications in automotive devices is given from various points of view. Design and manufacturing light weight devices for automotive vehicles is the primary focus field [24]. This author analyzed the various chemical storage tanks used in automotive and nonautomotive fields with various materials. It was done using ANSYS 19 software, and the results were compared with steel material [25]..Figure 2
Boundary conditions —rectangular domain.


### 1.1. Topology Optimization of Rectangular Domain

The boundary conditions of a rectangular domain are as shown in Figure2. Topology optimization can be implemented through the use of finite element methods for the analysis and optimization techniques based on the following methods.


### 1.2. Topology Generation

Table1 shows objective functions.Table 1
The objective functions of the rectangular domain after topology optimization.
Total elastic strain energy (J)Mass minimization (%)Output displacement (m)27.682500.066The figures show the topology generation of the general domain taken for analysis which is slowly distributed after various iterations (Figure3), and the final topology optimized design shows optimum material distribution in blue zones and material voids in red zones (Figure 3).Figure 3
Stress distribution after multiple iterations.The abovementioned table elucidates the increase in compliance and mass minimizations achieved through increased strain energy in the rectangular domain (Table1). The same procedure will be adopted and numerically analyzed in all three following mechanisms and robotics components.


## 1.1. Topology Optimization of Rectangular Domain

The boundary conditions of a rectangular domain are as shown in Figure2. Topology optimization can be implemented through the use of finite element methods for the analysis and optimization techniques based on the following methods.


## 1.2. Topology Generation

Table1 shows objective functions.Table 1
The objective functions of the rectangular domain after topology optimization.
Total elastic strain energy (J)Mass minimization (%)Output displacement (m)27.682500.066The figures show the topology generation of the general domain taken for analysis which is slowly distributed after various iterations (Figure3), and the final topology optimized design shows optimum material distribution in blue zones and material voids in red zones (Figure 3).Figure 3
Stress distribution after multiple iterations.The abovementioned table elucidates the increase in compliance and mass minimizations achieved through increased strain energy in the rectangular domain (Table1). The same procedure will be adopted and numerically analyzed in all three following mechanisms and robotics components.


## 2. Topology Optimization Design Application Devices

Based on the general topology optimization procedure (Figure1–4), the rectangular domain is optimized and objective functions also achieve mainly the optimum strain energy with mass minimization (Table 1). Also the volume reduction is converged quickly in components within minimum iterations (Figure 5).Figure 4
Final stress distribution plot.Figure 5
Volume reduction vs iterations.The major mechanical properties required for the abovementioned application are high flexibility, strength, durability, fatigue resistance, and excellent abrasion resistance [26−28]. Hence, three materials are chosen for their characteristic studies and synthesis. Some of the application parts are L-clamp plate and clutch clamp support plates. Hence, the objective function of mass minimization with optimum compliance is considered for taken mechanisms and robotic devices.Case – 1: the numerical analysis on L-clamp plate in both steel and ABS plastics to find the objective function after centric load application in domain and topology optimization.The previously shown pictorial images are of the 2D L-clamp plate with solid and topology optimized views. After optimization, we found the mass minimization to be around 60% of the original mass (Table2).The linear displacement after center force application and the corresponding stress and displacement (Figure6) in both the materials are analyzed based on mass minimization conditions (Table 2).Figure 6
Topology optimized compliant L-clamp plate (mild steel and ABS plastics).The following table shows the objective functions between steel optimized plate and ABS optimized plate.The model design of the abovementioned L-clamp is from the domain of a rectangular domain in which the solid material is topology optimized and voids as shown and stress distribution analyzed numerically in expansion mode (Figure7).Figure 7
Topology optimized compliant L-clamp displacement—Z direction.Case – 2: the numerical analysis on the clutch circular- clamp plate in both steel and ABS plastics to find the objective function after centric load application in the domain and topology optimization (Figure8).Figure 8
Topology optimized mechanism and robotics clamp plate design.The previous pictorial images are of 2D C clamp-plate with solid and topology optimized views. After optimization, we found the mass minimization was around 20% of the original mass (Table3).The linear displacement after center force application and the corresponding stress and displacement (Figure8) in both the materials are analyzed based on mass minimization conditions (Table 3).The following tabulation shows the C-clamp plate objective functions between optimized steel and ABS materials.The model design of the abovementioned C-clamp-plate is from the domain of a circular domain in which the solid material is topology optimized and voids as shown in Figure9 and stress distribution analyzed numerically in expansion mode (Figure 10).Figure 9
Topology optimized compliant C-clamp plate (mild steel and ABS plastics).Figure 10
Topology optimized compliant C-clamp plate displacement–Z direction.


### 2.1. Robotic Gripper Devices Topology Optimization

The model design of the abovementioned gripper device is from the domain of trapezium domain in which the solid material is topology optimized and voids as shown in Figure11 and stress distribution analyzed numerically in expansion mode (Figure 12).Figure 11
3D solid compliant robotic gripper.Figure 12
3D topology optimized compliant robotic – 42% volume reduction.Case- 3: based on the abovementioned 2 cases, the robotic magnetic gripper application is topology optimized for considerable volume reduction to handle easily and to achieve accuracy in pick and place functions.Speed and accuracy of the mechanisms and robotic functions by achieving the considerable mass minimization with less external load [29−31].


## 2.1. Robotic Gripper Devices Topology Optimization

The model design of the abovementioned gripper device is from the domain of trapezium domain in which the solid material is topology optimized and voids as shown in Figure11 and stress distribution analyzed numerically in expansion mode (Figure 12).Figure 11
3D solid compliant robotic gripper.Figure 12
3D topology optimized compliant robotic – 42% volume reduction.Case- 3: based on the abovementioned 2 cases, the robotic magnetic gripper application is topology optimized for considerable volume reduction to handle easily and to achieve accuracy in pick and place functions.Speed and accuracy of the mechanisms and robotic functions by achieving the considerable mass minimization with less external load [29−31].


## 3. Benefits of Compliant Material-Based Mechanism

The tangible benefits of topology optimization in compliant devices lead to direct mass reduction in the devices and make them easier to handle and fit into the applications. Geometric and mechanical advantage through topology optimization design, material cost is reduced and number of parts assembly is also reduced. The intangible benefits are efficiency increases in the vehicle performance without affecting safety. Design and development time are less for designers.


## 4. Results and Discussions

With reference to Figures5 to 9 and Tables 2 and 3, we elucidated the three different cases.Table 2
Objective functions —steel plate vs ABS plastic.
DescriptionMild steelABS plasticSizeL-40 mm, W-60 mm, H-40 mmL-40 mm, W-60 mm, H-40 mmThickness: 5 mmThickness: 5 mmMassInitial: 0.17 KgInitial: 0.023 KgAfter optimization: 0.071 kgAfter optimization: 0.009 kgDisplacementX-displacement– 0.008 mmX-displacement– 0.75 mmY-displacement– 0.07 mmY-displacement– 8 mmSafety factor1.75 min UL0.17 ULStress118 MPa (max)117 MPa (max)Table 3
Objective functions–steel plate vs ABS plastic.
DescriptionMild steelABS plasticSizeDiameter (Dia) 1–186 mm, Dia 2–126 mm, thick-18 mmDia 1–186 mm, Dia 2–126 mm, thick-18 mmLocating Dia: 44 mm,Locating Dia: 44 mm,MassInitial: 2.45 KgInitial: 0.33 KgAfter optimization: 1.96 kgAfter optimization: 0.26 kgDisplacementX-displacement – 0.000049 mmX-displacement – 0.0047 mmY-displacement – 0.00032 mmY-displacement – 0.029 mmSafety factor3 min UL7.27 ULStress2.32 MPa (max)2.2 MPa (max)Case - 1: in this condition, the L-clamp displacement in the X-direction is 90%, and the deflection is noticed in complaint material compared to mild steel at 10% (Figure13). Hence, in these robotic gripper applications, the compliant material can be used with less external force to avoid brittle cracks.Figure 13
Graphical proportion: topology optimized compliant materials vs mild steel.Case - 2: in this condition, the C-clamp displacement in the X-direction is 99%, and the deflection is noticed in the complaint material compared to mild steel at 1% (Figure13). Hence, this can be used in mass clamping and dynamic clutch engagement devices with lesser force applications.In all two cases, the mass reduction is 90% and is noticed in complaint material compared to mild steel whereas 10% (Figure13). Hence, for better efficiency and flexible applications, the compliant material part is best suitable.


## 5. Conclusions

Topology optimization and synthesis for general domain and relative applications are analyzed in this paper and based on analysis the surplus volume and mass reduction and in turn efficiency improvement in mechanism and robotics devices is fairly possible. Analysis is helpful to identify the high-stress areas in the compliant devices with various material characteristics to achieve less deformation without fatigue failure. An optimized shape and mechanical advantage of the product are achieved for desirable strength. The desirable volume and mass reduction (Table2) happens with the penalization method and following design synthesis of the application parts to be 3D printed through additive manufacturing technology for compliant flexural anchor, compliant gripper, and clutch clamp plate. Further the materialized parts will be experimentally tested and compared with numerical analysis objective functions and relative performance test of characteristics for its stability and rigidity. This formulation and design of topology optimization balance both the compliance and stiffness requirements and withstand the applied loads in these devices. Future work will induce numerical analysis comparison of component design with experimental part testing and part performance under loads. Thus, optimization technology and analysis are conducted to achieve desired objective functions without affecting safety.



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