Dynamic modeling of compliant constant-force compression mechanisms

TLDR: In this paper, a mathematical dynamic model is derived for compliant, constant-force compression mechanisms, based on the pseudo-rigid-body model simplification of the device, which allows every configuration to be represented by the same model, so a separate treatment is not required for each configuration.

About: This article is published in Mechanism and Machine Theory.The article was published on 2003-12-01 and is currently open access. It has received 108 citations till now. The article focuses on the topics: Compliant mechanism & Deflection (engineering).

Figures

Table 3: Mechanism parameters (parameters used directly in dynamic model are emphasized).

Figure 2. (a) Compliant constant-force mechanism, in its displaced state, and (b) its corresponding pseudo-rigid-body model.

Table 1: Test mechanism dimensions, material properties, and masses (parameters used directly in dynamic model equations are emphasized).

Figure 9. (a) Photograph of experimental setup for dynamic testing of constant-force mechanisms, and (b) schematic of experimental setup.

Figure 13. Frequency plots depicting the median force and peak-to-peak magnitude difference exhibited by the constant-force mechanism.

Figure 8. Constant-force test mechanism divided along its line of symmetry.

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "Dynamic modeling of compliant constant-force compression mechanisms" ?

In this paper, the pseudo-rigid-body model is used to obtain a viable dynamic model for the compliant constant-force mechanism. 

Q2. What is the torsional spring constant for a cantilever beam?

The torsional spring constant for a cantilever beam with a force at the free end is given by (3) where is the stiffness coefficient (a nondimensionalized torsional spring constant), is the modulus of elasticity of the flexible segment, and is the moment of inertia of the flexible segment. 

Q3. What are the common types of constant-force mechanisms?

Constant-force mechanisms are useful in applications requiring a constant force to be applied to a time-varying or non-uniform surface, such as grinding, swiping, deburing, welding, and assembly [9]. 

Q4. What is the way to optimize the constant force mechanism?

Depending on what attributes are most desirable – a wide frequency band with moderately low peak-to-peak force, asingle frequency with very low peak-to-peak force, or some other similar effect – the constant-force mechanism parameters can be optimized to achieve the desired results. 

Q5. How does the force of a constant-force mechanism work?

For the test device (heavy solid line), this occurs at about 99 rad/s.40 N 9.0 lbf( )3.5 N± 0.79± lbf( ) 6 N± 1.35± lbf( )18In few applications will it be useful to give a constant-force mechanism a displacement input by attaching an actuatoror surface directly to the slider; the two will usually be touching, but not rigidly connected. 

Q6. What is the simplest way to convert a cantilever to a rigid body?

Converting the mechanism to its rigid-body counterpart greatly simplifies kinematic and dynamic analysis by allowing the use of rigidbody modeling techniques. 

Q7. What is the reason for the higher relative error for these classes?

All four of the mechanisms tested have agoodness of fit of modeled to measured force of 83% or better, and most were over 95%.∆xb 0.40 r2 r3+( )=∆xb 0.40 r2 r3+( )= xb max xb minFnom 2 k3 r3 ----Φ=Fnom 2 k2 r3 ----Φ=The higher relative error for these classes between measured and modeled force than mechanism Class 1A-d The authorislikely due to considerably large deflection in the pin joints. 

Q8. What is the difference between the two types of mechanisms?

Test results show that all four mechanisms exhibit a range of frequencies over which the mechanism exhibits better constant-force behavior than at static conditions. 

Q9. What is the common method used to describe compliant mechanisms?

Lyon et al. [27] used the PRBM in conjunction with Lagrange’s method to develop linear ordinary differential equations that successfully described compliant parallel-guiding mechanisms. 

Q10. What is the difference between the peak-to-peak force plot and the static load?

This very interesting and unexpected discovery from the peak-to-peak force plot is that there exists a range offrequencies over which a constant-force mechanism exhibits better constant-force behavior than for static loading. 

Q11. What is the common approach to dynamic modeling?

Another approach to dynamic modeling is the work of Pascal and Gagarina [23], who discretized flexible components by a RayleighRitz procedure, and then numerically simulated the dynamic response using dynamical codes devoted to rigid multibody systems.