Scotch Yoke Design Analysis

Overview

In Phase I, our team conducted an initial evaluation and controlled teardown of the assigned product to understand its functionality, subsystems, and underlying mechanical design. We documented the disassembly process, identified major machine elements and mechanisms, and mapped how power and motion were transmitted through the system. Using this information, we defined clear analytical focus areas for Phase II by selecting critical components whose performance and sizing were central to the product’s operation.

In Phase II, our team performed a detailed engineering evaluation of the assigned product to assess the adequacy of its key machine elements through analytical and numerical methods. I was responsible for analyzing the scotch yoke mechanism, which included  developing free-body diagrams and applying fatigue theory and finite element analysis to evaluate stresses and potential failure modes under cyclical loading. The results were used to determine safety factors and validate design decisions. This analysis contributed to an integrated system-level discussion of how individual components interact to deliver the product’s overall function and highlighted both strengths and limitations in the original design.

Phase I - Product Teardown

To understand how the tool operates, our group worked together to disassemble the saw and isolate each of its parts. We first removed the housing and cover to get a clear view of the internal components. From there, we applied an external force that allowed us to manually rotate the gear and observe how the motor’s rotational motion is transformed into linear motion. We were able to see how the smaller bevel gear drives the larger bevel gear, in turn spinning the crank connected to the gear on the other side. This causes the yoke to oscillate, establishing the overall linear motion of the mechanism. After characterizing the mechanisms involved in this process, we selected specific machine elements for deeper analysis, including the spiral bevel gears, the two bearings mounted on the shaft, and the scotch yoke mechanism. These elements are central to the device’s performance because they drive the back-and-forth motion of the saw. Finally, we disassembled the rest of the product, isolating the mechanical components responsible for converting rotational motion into linear motion and creating an exploded view of the assembly.

Phase II - Scotch Yoke Analysis

Description

The main function of the Scotch yoke mechanism is to transform rotational motion to linear motion. This mechanism turns the rotational motion of the motor into the linear, push-and-pull motion of the blade. This component was chosen for analysis because it is the mechanism that gives the machine its functionality and serves as a load path through which cutting forces are transmitted. The specific portion of the yoke and crank that will be analyzed is the shaft that extends from the yoke and is responsible for holding the blade. 

Analysis

The material of the shaft connecting the blade and the yoke was assumed to be quenched and tempered 4140 steel since this material is used in a wide range of applications including connecting rods and shafts [1]. The corrected endurance limit for the material was determined using the Marin correction factors for the surface condition and loading case. 

Then, two free body diagrams depicting the two loading conditions experienced by the shaft were drawn to determine which forces needed to be analyzed. When the blade is moving toward the user, there is a cutting force acting on the blade in the opposite direction. This force places the blade in tension, which simultaneously places the shaft of the yoke in tension since they are connected via a pin. When the blade is moving away from the user, the blade is not cutting the workpiece, but there is a force of friction between the blade and the workpiece that acts opposite the direction of motion, placing the blade and the shaft of the yoke in compression. The force from the user pushing the saw into the workpiece is neglected since we are operating under the assumption that the user is allowing the saw's motion to carry itself down through the workpiece. 

To determine the cutting force Fc imposed on the blade, the mechanical cutting force model, Fc = Crbchc , was used [2]. 

One important parameter in Equation 1 is the cutting resistance or specific cutting resistance Cr which directly relates to the material of the workpiece. To obtain this value, the workpiece is assumed to be ash wood, which has an experimentally derived cutting resistance of 130 MPa [3]. 

Since the blade is only cutting when it is moving in the direction of the user, use of the reciprocating saw is a case of constant amplitude loading. In the max stress case, the cutting force acts on the shaft, whereas, in the minimum stress case, the friction between the blade and wood acts on the shaft. The stress that occurs due to the dynamic friction between the blade and the workpiece is so small it was assumed to be zero. Then, the stress-life approach was used to determine the alternating and mean stresses, which was then applied to the modified Goodman failure criterion to define a factor of safety for the shaft.  

Since this method of analysis does not allow for the assessment of the stresses experienced by the yoke, a simplified assembly was modeled in SolidWorks so that a static study could be conducted using SolidWorks FEA. This system consists of two components: the gear that functions as the crank portion of the Scotch yoke mechanism and the yoke. In reality the pin on the gear would have a bearing on it, but the intent of this study is to determine the stress reaction of the yoke to the cutting force, so the bearing was disregarded. 

The components were assigned mates to fully define the assembly at full extension of the blade, since this is where maximum stress is experienced by the component. The parameters implemented into the static study can be found in Table 2. Note that fixtures were assigned with the intent to limit motion that is not normally seen in the real mechanism. With this in mind, the yoke was assigned a reference geometry fixture to limit movement in and about the Y-axis since the real system does not see either type of this motion at this instant in time. 

Results

Given the cyclical loading of the reciprocating saw with a maximum force of 1305.66 N and minimum force of 0 N, the maximum and minimum stresses experienced by the shaft were determined to be 5.1 and 0 MPa respectively. This, along with the determination of the notch sensitivity and the fatigue stress concentration factor allowed for the calculation of the alternating and mean stresses, which were both equal to 3.81 MPa. Through a stress-life approach analysis of the shaft, the factor of safety was determined to be about 56. 

Figure 6 shows that the yoke sees the bulk of the stress concentration when the cutting force is applied to the end of the shaft, which makes sense due to the changing geometry and presence of sharp edges around this area. The majority of the stress seen in this region is around 3.040 · 108 N/m2  which provides a factor of safety of 3.58. 

Discussion

Such a high factor of safety across both the hand calculations and the FEA analysis demonstrates that the material selected for the yoke is more than adequate for the functionality of the tool. This safety factor could increase or decrease depending on the material of the shaft, since the actual material was not provided by the supplier. Another limitation of the analysis performed lies in the assumption that the blade is used properly, i.e. the user allows the blade to “carry itself” down through the workpiece as it cuts through the material.  In reality, a lot of users tend to push the blade down into the workpiece, which would add an additional force with components in the vertical and horizontal direction. Accounting for this additional force would add another stress into the problem that was not considered in this analysis, turning the problem into a combination of different loading modes rather than a singular loading case. Additionally, this reciprocating saw is advertised to be used for many different materials, but this analysis was only conducted for hardwood. Looking into different, tougher materials like metals or hard plastics would most likely lower the factor of safety due to the higher cutting force required to create chips.