WO2019240575A1

WO2019240575A1 - Mechanism with a rotatable crank

Info

Publication number: WO2019240575A1
Application number: PCT/NL2019/050354
Authority: WO
Inventors: Gregor Jan VAN DEN DOEL; Davood FARHADI MACHEKPOSHTI; Justus Laurens Herder
Original assignee: Technische Universiteit Delft
Priority date: 2018-06-14
Filing date: 2019-06-12
Publication date: 2019-12-19
Also published as: NL2021122B1

Abstract

Mechanism comprising a fully rotatable crank with a predefined crank length a, and a reciprocating input organ wherein a coupler link with a predefined coupler link length b connects the input organ to the crank, and wherein a spring- loaded arm extends sideways from the coupler link, wherein a spring connects the arm with the fixed world, and the spring connects to the arm at a position C distant from the coupler link.

Description

Mechanism with a rotatable crank

The invention relates to a mechanism comprising a ful ly rotatable crank, and a reciprocating input organ wherein a coupler link connects the slider to the crank. The input organ can for instance be a slider.

From PL 79 899 a crank slider mechanism is known com prising a fully rotatable crank, and a reciprocating slider wherein a coupler link connects the slider to the crank, wherein a spring-loaded arm extends away from the slider, and where in a spring connects the spring-loaded arm with the fixed world, and the spring connects to the spring-loaded arm at a position distant from the slider.

The history of crank slider mechanisms dates back to approximately 300 A.D. T. Ritti et al report on this in the article "A relief of a waterpowered stone sawmill on a sarcopha gus at hierapolis and its implications" in the Journal of Roman archaeology, 20: and 139 - 163, 2007.

Particularly since the introduction of steam engines the conversion of rotary motion into reciprocating motion or vice versa has been essential for industrial improvement, and this is where crank slider mechanisms come into play. The reciprocating motion of the slider creates two singularity points per cycle wherein no force transmission is possible between the crank and the coupler link. This is when the velocity of the slider is zero, which is also the point at which the slider changes motional direction. At this point energy transfer be tween the crank and the coupler link is zero. A problem is that in a larger area around the singularity points energy transfer between the crank and the coupler link may be insufficient at all to maintain the systems motion.

The conversion of rotary motion into reciprocating mo tion or vice versa is even nowadays still a challenge. One of the solutions that is proposed or applied to avoid the problem that at the singularity points and in the region around these singularity points no or insufficient energy transfer between the crank and the coupler link is possible, is to apply a fly wheel that is connected to the crank. This is however only a feasible solution for high-speed applications and goes at the expense of increased weight due to the flywheel.

It is an object of the invention to avoid the use of a flywheel, and to propose a solution to the singularity problem which is also feasible in low-speed applications, and which re quires no external energy input.

According to the invention a mechanism is proposed in accordance with one or more of the appended claims.

The invention applies in general to a mechanism comprising a fully rotatable crank, and a reciprocating input or gan (which may for instance be a slider or a back-and-forth moving driving arm) wherein a coupler link connects the input organ to the crank, wherein a spring-loaded arm extends side ways, and wherein a spring connects the spring-loaded arm with the fixed world, and the spring connects to the spring-loaded arm at a position distant from the input organ.

An essential aspect of the invention is that the spring-loaded arm extends sideways (oblique or at a right angle) from the coupler link and is unitary with the coupler link or is mounted on the coupler link so as to maintain a fixed orientation of the spring-loaded arm with reference to the cou pler link during operation when the crank of the mechanism ro tates. The (linear or rotary woundable) spring is used to store potential energy derived from the operation of the mecha nism itself, and thus avoids the use of external energy. The mechanism of the invention is therewith very suitable to be ap plied in a very diverse range of applications including micro mechatronics and energy harvesting.

The mechanism of the invention is thus preferably ar ranged such that the spring at least releases energy to drive the coupler link when the coupler link and the crank are in each other's extended direction. Preferably the release of en ergy by the spring should also occur in a larger region around the singularity areas of the mechanism.

Furthermore it is preferred that the spring stores en ergy at least in part in a region wherein the coupler link drives the crank or vice versa. Accordingly there is a closed energy balance in a single motion cycle of the mechanism of the invention .

Suitably the arm extends sideways from the coupler link at a position where the coupler link connects to the input organ with a revolution joint. The spring then connects to this sideways extending arm at a position distant from the revolu tion joint. This is however not the only feasible position. It is found that the benefits of the invention can be achieved in a mechanism wherein the crank has a predefined crank length a, and the coupler link has a predefined coupler link length b, when the position C distant from the coupler link at which the spring connects to the sideways extending arm is selected in a Cartesian axis system x, y wherein the origin of this axis sys tem x, y is in a revolution joint of the input organ with the coupler link, when the coupler link and the crank are in each other's extended direction, such that the following relations are satisfied:

- lambda . 1,5 . b <= x <= lambda . 1,5 b

0 <= y <= lambda . 2 b wherein lambda = b/a, and wherein the spring connects to the fixed world at a position distant from the position C which is selected such that the spring is capable to drive the coupler link at least when the coupler link and the crank are in each other's extended direction.

One of the further benefits of the invention is that it is sufficient that the spring is a single spring.

The invention will hereinafter be further elucidated with reference to the drawing of an exemplary embodiment of an apparatus according to the invention that is not limiting as to the appended claims.

In the drawing:

-figure 1 shows a schematic representation of a crank- slider mechanism according to the prior art;

-figure 2 shows a force transmission of the crank- slider mechanism of figure 1 with lambda = 6;

-figure 3 shows both singularity positions in a crank- slider mechanism of the prior art;

-figure 4 shows an indication of forces acting on the crank, from the slider and an alternative source;

-figure 5 shows a region with transmission angles that are ideal for storing or release of energy;

-figure 6 shows an example of an extension cycle of a translational spring with respect to time (t) ;

-figure 7 shows a schematic representation of a crank- slider mechanism according to the invention with an arm extend ing from the coupler link at a right angle and a spring con necting the arm to the ground;

-figure 8 shows a grid normalized to the length of the coupler link b, with the origin on the rotational joint of the slider with the coupler link; and

-figure 9 shows a schematic representation of a mecha nism according to the invention with a back-and-forth movable arm as input organ.

Whenever in the figures the same reference numerals are applied, these numerals refer to the same parts.

A. Singularity problems

Figure 1 shows a conventional crank slider mechanism comprising a fully rotatable crank with a predefined crank length a, and a reciprocating slider wherein a coupler link with a predefined coupler link length b connects the slider to the crank.

The kinematics of the crank-slider mechanism are based on the geometry of the links and the elevation of the slider. The transmission is defined by the ratio lambda between the length of the crank a and the length of the coupler link b, in dicated in figure 1. lambda = b/a (1)

To illustrate the problem of the singularity points, the force transmission of a crank-slider mechanism (with lambda = 6) is normalized and shown in figure 2. The input force F at the slider is considered constant.

The transmitted torque Ti at the output is calculated with the displacement xsl of the slider and the angle theta of the crank according to the following formula:

Ti (theta) = F . d(xsl)/d (theta) (2)

The problem becomes evident when a required output torque is considered and plotted in figure 2 (40% of the maximum transmitted torque, shown as black dashed line) .

The problem is not only limited to the singularity points. The regions around these points are also causing a problem. The main issue starts where the power input of the slider is insufficient and the slider is not able to transmit the required torque at the output (Ti < To) .

The input force of the slider will result in a lower torque between 151° - 208° and 339° - 20° indicated in figure 2 as the region between the arrows. The problematic regions are of course smaller when the required output torque is reduced. Therefore, the singularity problem can be defined as: "The re gion where the transmitted torque from the input is smaller than the required torque output , caused by the kinematics in combination with the required output load."

B. Design requirements

The difference in torque must be provided by another source to create a solution for this problem. The alternative source can be expressed as a force acting on the crank, shown in figure 4.

When the combined force of the alternative source and the slider is resulting in a higher torque than the required output torque, the singularity problems are solved. Therefore, passing through singularity is accomplished when a force trans mission is present at every point of the cycle. A drivable pay- load is then determined by a minimum torque which is always present in a full cycle motion of the crank slider mechanism.

An embodiment of the solution according to the invention shows figure 7, wherein a spring-loaded arm 3 extends sideways at a right angle from the coupler link 9, and wherein a spring 8 connects the sideways extending arm 3 with the fixed world 5, and the spring 8 connects to the sideways extending arm 3 at a position 6 (position C in figure 9 to be discussed hereinafter) distant from the coupler link 9. Figure 7 depicts not the only possible solution. Relevant for the invention is the location of position 6 or C at which the spring 8, which can be a single spring, connects to the arm 3 that is sideways extending from the coupler link 9. This said location of posi tion 6 or C at which the spring 8 connects to the arm 3 is well defined by arranging that the arm 3 is unitary with the coupler link 9 or is mounted on the coupler link 9 so as to maintain a fixed orientation of the spring-loaded arm 3 with reference to the coupler link 9 during operation when the crank 1 of the crank slider mechanism rotates. Within the aforesaid re

striction the arm 3 may for instance be extending obliquely from the coupler link 9. The exact location of the arm is therefore not decisive and can vary as long as the position 6 or C distant from the coupler link 9 at which the spring 8 con nects to the sideways extending arm 3 is well defined, and preferably selected in a Cartesian axis system x, y wherein the origin of this axis system x, y is in a revolution joint 4 of the slider 2 with the coupler link 9, when the coupler link 9 and the crank 1 are in each other' s extended direction (as shown in figure 8), such that the following relations are sat isfied:

- lambda . 1,5 . b <= x <= lambda . 1,5 b

0 <= y <= lambda . 2 b wherein lambda = b/a, a = crank length and b = the length of the coupler link, and wherein the spring 8 connects to the fixed world 5 at a position D distant from the position 6, C, which position D is selected to drive the coupler link 9 at least when the coupler link 9 and the crank 1 are in each other's extended direction.

Without adding other actuators, the crank slider mech anism of the invention is passive: the alternative power source mentioned with reference to figure 4 is generated by the input slider 2 itself.

Turning back to figure 2 a usable driving mechanism is expected to create a minimum output torque through a full cycle motion of at least 40% of the maximum torque, shown in figure 2. Theoretically, the highest possible constant output torque is 62.8% of the maximum torque (with lambda = 6}, equal to the average transmitted torque (Tavg) :

Tavg =F . 2a/ pi (3)

C . Passing through Singularity with Elastic Potential Energy

The elastic potential energy of the spring 8 is used to manipulate the force transmission in the crank-slider mecha nism. Storing energy in the spring 8 results in a negative torque on the crank 1 and the release of energy results in a positive torque.

The region where energy must be stored is determined by the kinematics of the crank-slider mechanism. The force transmission in a crank-slider mechanism shows two peaks (fig ure 2) . The regions around the peaks have a high transmission angle. The torque from the input is higher than the required output torque. Therefore, the excessive torque in these regions around the peaks is stored. In general, the peaks are located around crank angles of 90° and 270°. The ideal region for stor ing energy around a crank angle of 270° as indicated in figure 5(a). The transition point is located where the ideal region for storing energy ends.

The part where energy must be released from the spring 8 is around the singularity points (theta of 0° and 180°) .

Here,

the torque from the input is lower than the required output torque. The region around a crank angle of 0° is shown in figure 5 (b) .

D . Kinematic conditions

As mentioned the ideal storing and releasing of energy parts of the cycle are indicated at the crank-slider mechanism in figure 5. The challenge is to match these parts with the elastic potential energy cycle (EPEC) of the spring 8. The EPEC of a translational linear spring is determined by the change in relative distance of the connection points, referred to as the extension cycle. An example of the extension cycle for a translational spring is shown in figure 6. The spring must be ex tended in the same part of the cycle as indicated in figure 5(a), to store energy.

Likewise, the spring must be contracted in the corresponding part of the cycle, indicated in figure 5(b), to re lease energy.

With a rotational or rotary woundable spring, the EPEC is determined by the change in relative angle between two links .

The placement of the spring in the crank-slider mecha- nism is critical for the feasibility of the design. To create a working crank slider mechanism, the following two kinematic conditions are preferably met: (1) The EPEC of the spring must have two transition points; one for each singularity point. The transition point is where the spring changes from storing energy into releasing energy. With two transition points, the elastic potential energy cycle is divided into four parts; two parts for release of energy and two parts for energy storing.

(2) The singularity points must be in the energy release parts of the cycle.

E . Trajectory

With the stated kinematic conditions known, the place ment of the spring 8 is established for the configuration shown in figure 7 to find the desired elastic potential energy cycle. Without the use of additional links or linkages, the spring must be connected between one of the available links (crank, slider or coupler) or such a link and the ground. Every point on the crank-slider mechanism travels through a trajectory during the motion conversion. The shape of the trajectory deter mines the possibility of providing two transition points for translational springs. For rotational springs, the relative an gle between the links is used.

According to the invention it is preferable that the spring is attached between the coupler link and ground as shown in figure 7.

All the feasible connection points of the coupler link are investigated with a grid search. The grid search is con ducted with generalized coordinates [length c, angle delta] .

The configuration (theta = 0) of the crank-slider mechanism (lambda = 6) is used as a reference. The revolute joint 4 of the slider 2 is equalized with the origin {x = 0 , y = 0) of this Cartesian system. The grid is normalized to the length of the coupler link and shown in figure 8.

The distance between the revolute joint 4 of the slider 2 and position C at which the spring connects to the sideways extending arm is varying from 0 - 2b. The angle delta of the arm extending from the coupler link is varying from 0° - 360°. For each connection point of the coupler link the trajectory during operation of the crank slider mechanism is calculated, corresponding to the crank angle theta varying from 0° - 360°. The ground 5 connection of the spring 8 is placed on the midpoint of the line between the transition points. With the position of the connection points, the extension of the spring (xsp) is determined. Figure 8 as discussed above shows the area defining the possible locations of positions 6, C where the spring 8 connects to the sideways extending arm 3.

The spring characteristics (unstretched length, stiffness) are based on the required output load and the extension cycle of the spring. The spring constant (ksp) is determined from the difference between the maximum (Xmax) and minimum (Xmin) distance of the connection points. ksp = 2.Ws/ (Xmax - X in)² (4) wherein Ws represents the amount of energy (work) required to move a payload over the largest unfavourable region.

In case of the example of figures 1 and 2, the largest unfavourable region is 57° wide. This calculation ensures that enough energy can be stored in the spring 8 to move the mechanism through singularity. The unstretched length of the spring 8 is equal to the minimal distance between the connection points, to eliminate pretension in the system.

With the extension cycle and spring characteristics known, the force transmission of the spring is calculated:

Tsp(theta) = -0,5 . ksp . d (x2sp) /dtheta (5)

The torque from the spring (Tsp) is negative in the store of energy part, as the extension of the spring is in creasing. In contrast, the torque is positive in the release of energy part. The sum of the torques from the input force (equation 2) and the spring force, represents the total torque transmission. The minimum in the total torque transmission is equal to the maximum drivable payload.

Although the invention has been discussed in the fore going with reference to an exemplary embodiment of the apparatus of the invention, the invention is not restricted to this particular embodiment which can be varied in many ways without departing from the invention. An alternative construction shows for instance figure 9, wherein instead of a slider, a back-and- forth movable or reciprocating arm is applied as input organ 2. The mechanism is otherwise similar to the embodiment of figure 7, i.e. a spring-loaded arm 3 extends sideways at a right angle from the coupler link 9, and a spring 8 connects the side-ways extending arm 3 with the fixed world 5, wherein the spring 8 connects to the sideways extending arm 3 at a position 6 dis tant from the coupler link 9. As already mentioned hereinabove: relevant for the invention is the location of position 6 at which the spring 8, which can be a single spring, connects to the arm 3 that is sideways extending from the coupler link 9. This said location of position 6 at which the spring 8 connects to the arm 3 is well defined by arranging that the arm 3 is unitary with the coupler link 9 or is mounted on the coupler link 9 so as to maintain a fixed orientation of the spring- loaded arm 3 with reference to the coupler link 9 during opera tion when the crank 1 of the mechanism rotates. Within the aforesaid restriction the arm 3 may also in this embodiment for instance be extending obliquely from the coupler link 9. The hereinabove discussed exemplary embodiments shall therefore not be used to construe the appended claims strictly in accordance therewith. On the contrary the embodiments are merely intended to explain the wording of the appended claims without intent to limit the claims to these exemplary embodiments. The scope of protection of the invention shall therefore be construed in accordance with the appended claims only, wherein a possible am biguity in the wording of the claims shall be resolved using this exemplary embodiment.

Claims

1. Mechanism comprising a fully rotatable crank (1), and a reciprocating input organ (2) wherein a coupler link (9) connects the input organ (2) to the crank (1) , wherein a spring-loaded arm (3) extends sideways, and wherein a spring (8) connects the spring-loaded arm (3) with the fixed world (5), and the spring (8) connects to the spring-loaded arm (3) at a position (6, C) distant from the input organ (2), characterized in that the spring-loaded arm (3) extends sideways from the coupler link (9) and is unitary with the coupler link (9) or is mounted on the coupler link (9) so as to maintain a fixed orientation of the spring-loaded arm (3) with reference to the coupler link (9) during operation when the crank (1) of the mechanism rotates.

2. Mechanism according to claim 1, characterized in that the spring (8) at least releases energy to drive the coupler link (9) when the coupler link (9) and the crank (1) are in each other's extended direction.

3. Mechanism according to claim 1 or 2, characterized in that the spring (8) stores energy at least in part in a re gion wherein the coupler link (9) drives the crank (1) or vice versa .

4. Mechanism according to any one of claims 1 - 3, wherein the crank (1) has a predefined crank length a, and the coupler link (9) has a predefined coupler link length b, characterized in that the position (6, C) distant from the coupler link (9) at which the spring (8) connects to the sideways extending arm (3) is selected in a Cartesian axis system x, y wherein the origin of this axis system x, y is in a revolute joint (4} of the input organ (2) with the coupler link (9) when the coupler link (9) and the crank (1) are in each other's ex tended direction, such that the following relations are satisfied:

- lambda . 1,5 . b <= x <= lambda . 1,5 b

0 <= y <= lambda . 2 b wherein lambda = b/a, and wherein the spring (8) connects to the fixed world (5) at a position distant from the position (6, C) which is selected to drive the coupler link (9) at least when the coupler link (9) and the crank (1) are in each other's extended direction.

5. Mechanism according to any one of claims 1 - 4, characterized in that the spring (8) is a single spring.

6. Mechanism according to any one of claims 1 - 5, characterized in that the input organ (2) is one of a slider and a driving arm.