# Reverse Engineering and Topology Optimization for Weight-Reduction of a Bell-Crank
## 1 Introduction  
A bell crank is a mechanical component that is primarily responsible for translating the motion of links through an angle. It acts as a link between a spring and a damper component at one end, and a pushrod/pull rod at the opposing end. The most common limitation associated with vehicle suspension in racing vehicles is the inability to mount the spring/damper mechanism vertically, compared with most ordinary cars. As a result, bell cranks are incorporated into the design of racing vehicles to translate the vertical motion of the wheel into horizontal motion to allow the suspension to be mounted transversely or longitudinally [1].  
However, in racing vehicles, there are limitations on bell cranks that relate to their weight. When there is a limit in engine power capacity, a reduction in vehicle mass will improve the performance aspect of a racing vehicle known as a power-to-weight ratio. Hence, engineers are constantly trying to improve the performance of bell crank by reducing its weight, while maintaining its structural integrity. To achieve that, engineers have been using the structural topology optimization method to find an optimal material distribution in a structural design domain considering an objective function in presence of constraints [2; 3; 4; 5].  
However, only a limited number of studies in the literature examined topology optimization of bell cranks [4; 6; 7]. [PERSON] [6] used a topology optimization method to assess weight reduction of bell cranks for a Formula Society of Automotive Engineers (SAE) vehicle. The author considered reducing the mass of the rear bell crank component by at least 10% while maintaining the yield strength of the previous design. The author utilized destructive testing on three specimens under static loads of 445 N to validate their new design. [PERSON] et al. [4] used a 'Fully Stressed Design' optimization procedure to achieve the mass and stress optimization of bell crank of Formula SAE vehicle from SRM University Chennai in India. The procedure allowed them to investigate and analyze the structural stress distribution of the bell crank in real-time conditions during the damping process and the spring actuation. The authors managed to produce an optimized computer aided design (CAD) bell crank model with a 22% and 20% of overall weight and stress reduction, respectively.  
When reducing the mass (or volume) of a mechanical component such as bell cranks, engineers face challenges to maintain structural integrity. The structural integrity relevant to a mechanical component is its overall stiffness. An element that directly correlates with component stiffness is its natural frequency. The natural frequency of a certain vibration mode can be controlled in order to reduce the displacement or deformation of a particular point in the structure [8; 9]. [PERSON] et al. [10] found that chassis stiffness is directly related to its flexibility when the stiffness of the chassis increases, the twist vibration decreases and the overall vehicle handling is improved by allowing the suspension components to control a larger percentage of the vehicle's kinematics.  
No studies in the literature have utilized a non-destructive mode shape analysis to investigate the dynamic response of the bell crank. The benefit of using mode shape analysis is that it allows engineers to determine the dynamic stiffness of a structure. By changing the stiffness of the structure, engineers could minimize the amount of vibration, which is produced by the relative motion or deformation of the structure under applied loads [11]. In the case of the bell crank, a small relative motion in the suspension system will provide undesirable feedback to the operator in either lateral, longitudinal or cyclic loadings [12].  
The purpose of this study is to propose a methodology that incorporates a reverse engineering technique and physical testing for accurately and efficiently assessing topology optimization problems.