Structural synthesis of ancient Chinese original crossbo · Transactions of the Canadian Society for Mechanical Engineering, Vol. 37, No. 2, 2013 259 STRUCTURAL SYNTHESIS OF ANCIENT

Transactions of the Canadian Society for Mechanical Engineering, Vol. 37, No. 2, 2013 259

STRUCTURAL SYNTHESIS OF ANCIENT CHINESE ORIGINAL CROSSBOW

Kuo-Hung Hsiao

Collections and Research Division, National Science and Technology Museum, Kaohsiung, Taiwan

E-mail: [email protected]

Received January 2013, Accepted March 2013

No. 13-CSME-03, E.I.C. Accession 3461

ABSTRACT

The original crossbow was one of the most important weapons in ancient China. Since crossbows have

diversified types and were widely used in ancient China after the Spring and Autumn Period (770-476

BC), the original crossbow should have many designs in different eras and regions. The aim of this work

is to synthesize mechanism structures of the original crossbow. Based on the analyses of crossbows, the

structural characteristics and design constraints of this device are concluded. Then, according to the

concepts of generalization and specialization subject to the concluded design constraints, twelve feasible

structures of mechanism that meet the technological standards of the subject’s time period are

reconstructed.

Keywords: crossbow; structure of mechanism; reconstruction design; history of machinery.

SYNTHÈSE DES STRUCTURES D’UNE ANCIENNE ARBALÈTE CHINOISE

RÉSUMÉ

L’arbalète originale était l’une des plus importantes armes de guerre dans la Chine antique. Étant donné

qu’il y a plusieurs types d’arbalètes, et qu’elles étaient largement utilisées dans la Chine antique après la

période Printemps/Automne (770-476 avant notre ère), l’arbalète originale devait être différente selon les

époques et les régions. Le but de ce travail est de faire une synthèse des structures mécaniques de

l’arbalète originale. En se basant sur l’analyse des arbalètes, les caractéristiques de structure et de

contraintes de conception sont établies. Ensuite, selon les concepts généraux et spécifiques, en tenant

compte des contraintes, douze structures de mécanismes possibles, qui rencontrent les standards

technologiques de l’époque, ont été construites.

Mots-clés : arbalète; structure mécanique; concept de reconstruction; histoire des machines.

260 Transactions of the Canadian Society for Mechanical Engineering, Vol. 37, No. 2, 2013

NOMENCLATURE

KBB Bamboo

KCB Bow

KF Frame

KI Input link

KL Connecting link

KPL Percussion link

KT Thread/bowstring

J Number of joints

JA Cam joint Pxyz

RxyzJ An unconstrained pairing element

JBB Bamboo joint

JP Prismatic joint

J Py

Joint translates along y-axis

J Pyz

Joint translates along y and z axes

J Pxyz

Joint translates along x, y and z axes

JR Revolute joint

JRx Joint rotates about x-axis

JRxyz Joint rotates about x, y and z axes

JRz Joint rotates about z-axis Pz

RxJ Joint translates along z-axis and rotates about x-axis

Px

RyzJ Joint translates along x-axis and rotates about y and z axes

JT Thread joint

N Number of links

1. INTRODUCTION

According to the literatures and the excavations, ancient Chinese crossbows have three types

including the original crossbow, Chu State repeating crossbow and Zhuge repeating crossbow. An

original crossbow is a weapon bow mounted on a stock with a trigger mechanism for holding the drawn

bowstring as shown in Fig. 1 [1]. It was the standard military issue of the ancient Chinese arsenal. The

earliest one was found in the tomb at Qufu, Shangdong Province and dated to the 6th century BC [2]. The

trigger mechanism was designed in such a way that it was able to store a large amount of energy within

the bow when drawn, but was easily fired with little recoil when the input link was pulled. It also allowed

the shooter to aim the target for precision shooting. The shooting process of crossbow includes three

steps: drawing the bowstring, placing the bolt and shooting the bolt. A repeating crossbow is a crossbow

where the separate actions of three steps can be accomplished with a simple one-handed movement while

keeping the crossbow stationary. This allows a higher rate of fire than an original crossbow. Based on the

archeological finds, the repeating crossbow first appeared around 400 BC in the tomb in Hubei Province

as shown in Fig. 2 [3]. The magazine fixes on the top of the stock and contains twenty bolts, and the

device is worked by moving the input link forward and backward. Two bolts can be shot at once in the

reciprocating motion of the input link. Since the tomb belonged to Chu State during the War States

Period (722-481 BC), the device was named Chu State repeating crossbow. The Records of the Three

Kingdoms mentions another type of repeating crossbow named “Zhuge repeating crossbow” and

describes the strategist Zhuge Liang (181-234 AD) of the Three Kingdoms Period (220-280 AD) as the

inventor [4]. Figure 3 is a Zhuge repeating crossbow in the book of Treatise on Armament in the Ming

http://en.wikipedia.org/wiki/Bow_string

http://en.wikipedia.org/wiki/Repeating_crossbow#cite_note-0


http://en.wikipedia.org/wiki/Quarrel

http://en.wikipedia.org/wiki/Crossbow

http://en.wikipedia.org/wiki/Hubei


http://en.wikipedia.org/wiki/Records_of_the_Three_Kingdoms

http://en.wikipedia.org/wiki/Records_of_the_Three_Kingdoms

http://en.wikipedia.org/wiki/Strategist

http://en.wikipedia.org/wiki/Three_Kingdoms

http://en.wikipedia.org/wiki/Zhuge_Liang


Dynasty (1368-1644 AD) [1]. The magazine contains a number of bolts and functions as a percussion

link. The function of the percussion link with the magazine is to draw and release the bowstring to shoot

the bolt. When the device is worked by moving the input link, one or several bolts can be shot at once in

the oscillating motion of the input link. Since the types of crossbows were diversified and widely used in

ancient China, the structures of each crossbow should have many designs in different eras and regions. In

order to realize the development of ancient Chinese crossbows, it is necessary to study further for

accessing and understanding the real ancient technology.

Fig. 1. An original crossbow [1]

(a) Actual excavation (b) Structure

Fig. 2. Chu State repeating crossbow [3]

Fig. 3. Zhuge repeating crossbow [1]

K C B (2)

K F (1)

K P L (5)

K T (3)

K I (4)

K F (1)

K C B (2)

K F (1)

K P L (5)

K T (3)

K I (4)

K F (1)


The purpose of this work is to synthesize all feasible structures of the original crossbow. In what

follows, the mechanism structures of ancient Chinese crossbows are analyzed first. And, the

representation of joints of ancient mechanisms is presented. Then, an approach for synthesizing the

structures of ancient mechanisms with diversified types is introduced. Finally, the structural synthesis of

the original crossbow is provided.

2. STRUCTURAL ANALYSIS OF ANCIENT CHINESE CROSSBOW A mechanism which encounters a certain changes in its topological structure during operation is

called a reconfigurable mechanism. The topological structures of a crossbow are different during

shooting process. Therefore, ancient Chinese crossbow is a reconfigurable mechanism. It can be

normally treated as a kinematic chain with variable architectures depending upon the inherent topology

variability. Such chain is namely a variable kinematic chain or variable chain in short. Either from the

aspect of overall structure or the interior connectivity, a mechanism will topologically be a variable chain

if the arrangement of this chain is changeable.

The original crossbow and Chu State repeating crossbow generally consist of six members including

the frame KF(1), the bow KCB(2), the bowstring KT(3), the input link KI(4), the percussion link KPL(5) and

the connecting link KL(6) as shown in Figs. 1 and 2. The structure of Zhuge repeating crossbow is

simplified and the number of members is five without the connecting link as shown in Fig. 3. According

to topology variability, the operations of ancient Chinese crossbows can be divided into the following

four stages:

1. The undrawn stage

The purpose of this stage is to draw the bowstring. The bow and the bowstring are temporarily

immovable, Figs. 4(a1), (b1) and (c1). Then, the input link, the percussion link and the connecting link are

adjusted such that the bowstring can be properly drawn. When the bowstring is drawn instantly, the

operation enters the second stage.

2. The drawing stage

Since the bowstring is forced to complete the drawing by the shooter’s hands in the original crossbow,

the parts of trigger mechanism can be treated as to be incorporated with the frame, Fig. 4(a2). However,

the bowstring is automatically hooked through the operation in the repeating crossbow, Figs. 4(b2) and

(c2). When the bowstring completed the drawing, the operation enters into the next stage.

3. The drawn stage

When the shooter had drawn the bowstring and placed the bolt, the shooter can aim the target for

precision shooting in the original crossbow, Fig. 4(a3). However, the bolt falls from the magazine by

gravity in the repeating crossbow. When the bowstring is drawn in the maximum position, the percussion

link is adjacent to the frame in Chu State repeating crossbow, Fig. 4(b3) and the bowstring is adjacent to

the frame directly in Zhuge repeating crossbow, Fig. 4(c3). When the input link is driven and the

bowstring is released, the operation enters into the next stage.

4. The shooting stage

Through the elasticity of the bow and the bowstring, the bolt starts to be forced at this stage. Until the

bolt is shot away, the bow and the bowstring return to the original position and the function cycle will be

periodically continued. In addition, the input link, the percussion link and the connecting link can be

treated as to be incorporated with the frame, Figs. 4(a4), (b4) and (c4).

3. REPRESENTATION OF JOINTS Through the study of ancient mechanisms no matter in drawings or excavations, the joints can be

classified into three types including joints that are easy to identify such as gear joints and wrapping joints,

joints that are uncertain, and joints that are certain but are rare in modern kinematics of mechanisms.


(a1) (a2) (a3) (a4)

(a) Original crossbow

(b1) (b2) (b3) (b4)

(b) Chu State repeating crossbow

(c1) (c2) (c3) (c4)

(c) Zhuge repeating crossbow

Fig. 4. The variable kinematic chains of ancient Chinese crossbows

Since some special joints in ancient mechanisms can not be represented by modern schematic

representations, a novel representation for such joints in ancient mechanisms is introduced here [5, 6].

The number of degrees of freedom is the number of independent parameters needed to specify the

relative positions of the pairing elements of a joint. An unconstrained pairing element has six degrees of

freedom including three translational and three rotational degrees of freedom. And, a joint is represented

as xyz

xyz

P

RJ in which the superscript

xyzP denotes that it can translate as a prismatic joint (JP) along x, y and z

axes; and the subscriptxyzR denotes that it can rotate as a revolute joint (JR) about x, y and z axes. When a

pairing element connects to another pairing element and forms a joint, a constraint is imposed and the

motion of the original member is reduced by one or more degrees of freedom. Hence, a joint has a

maximum of five degrees of freedom and a minimum of one degree of freedom. For example, jointxRJ

represents that a pairing element of a joint can rotate about x-axis with respect to the other pairing

element. Joint zpJ represents that a pairing element of a joint can translate along z-axis with respect to the

other pairing element. And, joint x

yz

P

RJ represents that a pairing element of a joint not only translates along

x-axis and also rotates about y and z axes with respect to the other pairing element.

Figure 5(a) shows a two-member mechanism with a joint from the book of Chinese Technology in the

Seventeenth Century [7]. Since the drawing is not clear, link KL is adjacent to frame KF with an uncertain

joint. Considering the type and the direction of motion of the link, the joint has two possible types: the

link rotates about z-axis only, denoted asRzJ ; and, the link rotates not only about z-axis but also translates

along x-axis, denoted as Px

RzJ . The x and y axes are defined as the horizontal and vertical directions in the

drawing, respectively. The z-axis is determined by the right-hand rule.


(a) (b)

Fig. 5. Special joints in ancient mechanisms [7]

Thread and bamboo often appear as members in ancient mechanisms especially in textile and

agricultural devices. Figure 5(b) shows that bamboo KBB is adjacent to frame KF and thread KT

from the

book of Chinese Technology in the Seventeenth Century [7]. The bamboo is firmly fixed to the frame

and the thread ties the bamboo directly. The bamboo possesses elasticity and can go back to the original

position after using. The motion of the bamboo can be regarded as a link adjacent to the frame with a

revolute joint. The joint incident to the bamboo and the frame is defined as a bamboo joint, denoted as

JBB. Using a thread tying a member to form a joint is rare in modern mechanisms but popular in ancient

mechanisms. The joint incident to the thread and a member is defined as a thread joint, denoted as JT.

4. DESIGN APPROACH Figure 6 shows the process for synthesizing all feasible structures of ancient mechanisms with

diversified types [5, 8-11]. Each step of the process is explained as follows:

Step 1. Analyses of the structures of mechanisms

By analyzing the structure of a target mechanism, its structural characteristics are concluded including

the possible number of members and incidences among members and joints of the device. Since the

development of the similar mechanisms should influence each other, the structures of different devices

with the same function are usually alike. Therefore, the number of members and the structures of joints

of the relevant mechanisms can be considered. For example, ancient Chinese crossbows have three types.

One’s structural characteristics may be the other one’s design constraints.

Step 2. Generalized chains

The second step is to obtain or identify the atlas of generalized chains with the same numbers of

members and joints subject to concluded structural characteristics based on the concept of number

synthesis [12-13]. Generalization is to transform the mechanism, that involves various types of members

and joints, into a generalized chain with only generalized links and joints. A generalized link is a link

with generalized joints; it can be a binary link, ternary link, quaternary link, …etc. A generalized joint is

a joint in general; it can be a revolute joint, prismatic joint, spherical joint, or others. When several

members are connected by joints, they are said to form a chain. Graphically, a joint is symbolized by a

small circle, and a member with i incident joints is symbolized by an i-side shaded polygon with small

circles as vertices. Some of the important atlases of generalized chains have already been built in

references [12-13].


Fig. 6. Process for structural synthesis of ancient mechanisms with diversified types

Step 3. Specialized chains

Specialization is to assign specific types of members and joints in the available atlas of generalized

chains, subject to required design constraints [12-13]. Design constraints are defined based on the

concluded structural characteristics. And, a generalized chain after specialization is a specialized chain.

Based on the process of specialization, all possible specialized chains can be identified after assigning the

types of members and joints subject to the concluded design constraints for each generalized chain

obtained in step 2.

Step 4. Specialized chains with particular identities

In order to represent the structure of mechanism, a right-hand rectangular Cartesian coordinate system

is defined to describe each motion axis of the joints. By studying the target device, the function of the

device is determined. In view of the device function, these uncertain joints can be represented by

different types of joints to achieve the equivalent function. Considering the types and the motion

directions of the uncertain joints, all possible types of the uncertain joints are generated. By assigning the

possible types of the uncertain joints to the specialized chains obtained in step 3, specialized chains with

particular identities are obtained.

Step 5. Feasible designs

According to the motion and function requirements of the device, all feasible designs that meet the

technological standards of the subject’s time period can be obtained from the specialized chains with

particular identities.

5. STRUCTURAL SYNTHESIS According to the literature and the actual excavation, the original crossbow comprises six members

including the frame, a bow, a bowstring, an input link, a percussion link and a connecting link. And, it

has eight joints including one bamboo joint (JBB), two threat joints (JT), two cam joints (JA) and three

revolute joints (JRz). Since the original crossbow was popular and widely used in different eras and

regions, the structures of the original crossbow should have different designs. Furthermore, through the

integrating with geometry and kinematics, the trigger mechanism without the connecting link still has the


function of pulling bowstring by the percussion link, like Zhuge repeating crossbow with five-member

and six-joint. Therefore, the number of members of the original crossbow should be five or six. All

feasible structures of the original crossbow are synthesized through the following steps to illustrate the

introduced approach shown in Fig. 6:

Step 1. The structural characteristics of the device are:

1. It is a cam mechanism with five-member and six-joint or six-member and eight-joint.

2. The frame (KF) is a multiple link and adjacent to a pair of binary links.

3. The bow (KCB) is a binary link and adjacent to the frame (KF) with a bamboo joint (JBB).

4. The bowstring (KT) is a binary link and adjacent to the bow (KCB) with a thread joint (JT).

5. The input link (KI) is adjacent to the frame (KF) with a revolute joint (JRz) and is not adjacent to the

bowstring (KT).

6. The percussion link (KPL) is adjacent to the frame (KF) with an uncertain joint.

7. The connecting link (KL) is adjacent to the percussion link (KPL) and the input link (KI) with

uncertain joints.

Step 2. Since this is a device with five-member and six-joint or six-member and eight-joint, the

corresponding generalized chains are shown in Fig. 7, in which N is the number of links and J is the

number of joints.

(a1) (a2)

(a) N=5, J=6

(b1) (b2) (b3)

(b4) (b5) (b6)

(b7) (b8) (b9)

(b) N=6, J=8

Fig. 7. Atlas of some generalized chains with five and six members


Step 3. There must be a pair of binary links as a bow and a bowstring. And, the pair of binary links

must be adjacent to a multiple link as the frame. Therefore, only four generalized chains shown in Figs.

7(a2), (b3), (b4) and (b6) are qualified for the process of specialization. And, all possible specialized

chains are identified as follows:

Frame --- link KF

Since there must be a multiple link as the frame (KF) and a pair of binary links is adjacent to the

frame, the frame is identified as follows:

1. For the generalized chain shown in Fig. 7(a2), the assignment of the frame (KF) generates one non-

isomorphic result, Fig. 8(a1).

2. For the generalized chain shown in Fig. 7(b3), the assignment of the frame (KF) generates two results,

Figs. 8(a2) and (a3).

3. For the generalized chain shown in Fig. 7(b4), the assignment of the frame (KF) generates one non-


4. For the generalized chain shown in Fig. 7(b6), the assignment of the frame (KF) generates one non-


Therefore, five specialized chains with identified frame (KF) are available as shown in Figs. 8(a1)-(a5).

Bow and bowstring --- link KCB and link KT

Since there must be a pair of binary links as the bow (KCB) and bowstring (KT), and the bow is

adjacent to the frame and the bowstring with a bamboo joint (JBB) and a thread joint (JT), the bow and the

bowstring are identified as follows:

1. For the case shown in Fig. 8(a1), the assignment of the bow (KCB) and the bowstring (KT) generates one

result, Fig. 8(b1).


result, Fig. 8(b2).


result, Fig. 8(b3).


result, Fig. 8(b4).


result, Fig. 8(b5).

Therefore, five specialized chains with identified frame (KF), bow (KCB) and bowstring (KT) are

available as shown in Figs. 8(b1)-(b5).

Input link --- link KI

Since there must be an input link (KI) that is adjacent to the frame (KF) with a revolute joint (JRz) and

not adjacent to the bowstring (KT), the input link is identified as follows:

1. For the case shown in Fig. 8(b1), the assignment of the input link (KI) generates one result, Fig. 8(c1).

2. For the case shown in Fig. 8(b2), the assignment of the input link (KI) generates one result, Fig. 8(c2).

3. For the case shown in Fig. 8(b3), the assignment of the input link (KI) generates two results, Figs. 8 (c3)

and (c4).

4. For the case shown in Fig. 8(b4), the assignment of the input link (KI) generates one non-isomorphic

result, Fig. 8(c5).

5. For the case shown in Fig. 8(b5), the assignment of the input link (KI) generates one non-isomorphic

result, Fig. 8(c6).

Therefore, six specialized chains with identified frame (KF), bow (KCB), bowstring (KT) and input link

(KI) are available as shown in Figs. 8(c1)-(c6).

Percussion link and connecting link --- link KPL and link KL


Since the percussion link (KPL) must be adjacent to the frame (KF) and the input link (KI) with

uncertain joints and the remaining one is the connecting link, the percussion link and the connecting link

are identified as follows:

1. For the case shown in Fig. 8(c1), the assignment of the percussion link (KPL) generates one result, Fig.

8(d1).

2. For the case shown in Fig. 8(c2), the assignment of the percussion link (KPL) and the connecting link

(KL) generates one result, Fig. 8(d2).



4. For the case shown in Fig. 8(c4), there is no the connecting link (KL) that is adjacent to the input link

and the percussion link, Fig. 8(c4) is not qualified for the process of specialization.





Therefore, five specialized chains with identified frame (KF), bow (KCB), bowstring (KT), input link

(KI), percussion link (KPL) and connecting link (KL) are available as shown in Figs. 8(d1)-(d5). However,

the connecting link (KL) in Fig. 8(d2) and the percussion link (KPL) in Fig. 8(d4) are redundant during

shooting process. This means that Figs. 8(d2) and (d4) degenerate into five members. Therefore, these two

specialized chains are not feasible.

(f1) (f2)

(f3) (f4) (f5) (f6) (f7)

(f8) (f9) (f10) (f11) (f12)

Fig. 8. Structural synthesis of the original crossbow


(a1) (a2) (a3) (a4) (a5)

(b1) (b2) (b3) (b4) (b5)

(c1) (c2) (c3) (c4) (c5) (c6)

(d1) (d2) (d3) (d4) (d5)

(e1) (e2)

(e3) (e4) (e5) (e6) (e7)

(e8) (e9) (e10) (e11) (e12)

Fig. 8. Structural synthesis of the original crossbow (cont.)


(g)

Fig. 8. Structural synthesis of the original crossbow (cont.)

Step 4. The coordinate system is defined as shown in Fig. 1. The function of the trigger mechanism is

to pull the input link and release the bowstring to shoot through the transmission of the percussion link

and connecting link. The uncertain joints may have multiple types to achieve the equivalent function.

Considering the uncertain joints J1 and J2, each one has two possible types and they can not be the

same type simultaneously. When any one joint rotates in z-axis, denoted as JRz, the other one is a cam

joint, denoted as JA.

Considering the uncertain joint J3, it has two possible types. If J3 is a revolute joint, denoted as JRz, J4

must be a cam joint, denoted as JA. And, J5 and J6 have two possible types and they can not be the same

type simultaneously. When any one joint rotates in z-axis, denoted as JRz, the other one is a cam joint,

denoted as JA.

If J3 is a cam joint, denoted as JA, J4, J5 and J6 have two possible types. When any one is a cam joint,

denoted as JA, the others rotate in z-axis, denoted as JRz.

By assigning the possible types of the uncertain joints J1(JRz and JA), J2(JRz and JA), J3 (JRz and JA), J4

(JRz and JA), J5 (JRz and JA) and J6 (JRz and JA) to the specialized chains shown in Figs. 8(d1), (d3) and (d5),

twelve specialized chains with particular identities as shown in Figs. 8(e1)-(e12) are obtained.

Step 5. Figures 8(f1)-(f12) show the corresponding 3D solid models of the feasible designs. Figure 8(g)

shows a prototype of the original crossbow.

6. CONCLUSIONS The original crossbow is a reconfigurable mechanism and was dated back to 600 BC in ancient China.

Since crossbows were popular and widely used in ancient China, the structures of the original crossbow

should have many designs. Through the study of mechanisms and applying the concepts of

generalization and specialization of mechanisms subject to the concluded design constraints, all feasible

specialized chains are generated. By assigning the possible joints to the feasible specialized chains, all

possible structures of the original crossbow are systematically synthesized. The proposed approach not

only can be applied to the original crossbow but also to other ancient mechanisms with diversified types.


ACKNOWLEDGEMENTS

The author is grateful to the National Science Council (Taipei, Taiwan) under Grant NSC 101-2218-

E-359-001- for the financial support of this work.

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http://en.wikipedia.org/wiki/Zhuge_Liang

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Structural synthesis of ancient Chinese original crossbo · Transactions of the Canadian Society for Mechanical Engineering, Vol. 37, No. 2, 2013 259 STRUCTURAL SYNTHESIS OF ANCIENT