Peg-in-Hole under State Uncertainties via a Passive Wrist Joint with
Push-Activate-Rotation Function
Toshihiro Nishimura, Student Member, IEEE,
Yosuke Suzuki, Member, IEEE, Tokuo Tsuji, Member, IEEE, and Tetsuyou Watanabe, Member, IEEE

Abstract— This study presents a novel passive wrist joint withpush-activate-rotation (PAR) functionality for a peg-in-holeassembly and a strategy utilizing the passivity and inherent
functionality of the wrist. The PAR function involves rotation
around a vertical axis, automatically activated by pushing thewrist in the vertical direction. The novel features of the approach
are that 1) hardware based passive compliance absorbs
uncertainties of the states for the peg, 2) no active rotational
joints are required for the manipulator part, 3) F/T sensors are
not used; instead, an IMU sensor is, and 4) multiple shapes forthe peg or hole are available e.g., rectangular, circular, hexagonal,
and triangular prisms. The validity of the approach is shown via
several experiments.

I. INTRODUCTION
Peg-in-hole is one of the most fundamental assembly tasks
in robotic manipulations, and much effort has been directed
towards finding improved approaches [1][2][3][4][5]. Mainly,
approaches for realizing practical tasks are divided into
software and hardware compliances. The software-based
approach utilized Force/Torque (F/T) sensory information[6][7][8][9]. Kim et al. proposed an algorithm for conducting
tasks despite large positional and directional errors with F/Tsensors [6]. Chung et al. realized a fixtureless peg-in-hole for ahighly uncertain environment utilizing the F/T sensory
information with two manipulators [7]. In [8], two types ofimpedance controllers were proposed for a peg-in-hole method.
Jasim et al. proposed the methodology to determine theposition of the hole using a force sensor [9]. Visual sensors arealso popularly utilized for peg-in-hole problems [10][11][12].
Huang et al. presented a fast peg-in-hole strategy with visualcompliance [10][11]. Su et al. presented a sensor-less peg-inhole strategy for an eccentric peg such as a crankshaft based on
visual information [12]. Some approaches combined F/T andvisual sensors [13][14]. Song et al. presented a peg-in-holemethodology involving complex shapes with a F/T sensor andan eye-in-hand-camera [13]. Kim et al. proposed an assembly
strategy where a vision system was used for pose estimation
while force control was used for the procedure itself [14]. F/T
information for peg-in-hole can be estimated from torque input
to manipulators by an observer [15]. Polverini et al. presented
a sensor-less approach based on the observer [16]. Park et al.
proposed a strategy inspired by human behavior without F/Tsensors [17]. Recently, they extended the strategy utilizing the*
Research partly supported by NEDO.
T. Nishimura is with the Graduated school of Natural science andTechnology, Kanazawa University, Kakuma-machi, Kanazawa, 9201192
Japan (e-mail: to.nishimura@stu.kanazawa-u.ac.jp).

assistance of manipulators [18]. Matsuno et al. developed a
trajectory switching generator with a free wrist joint for
inserting a long peg into a tandem shallow hole [19]. The
strategies requiring no F/T sensors [16][17][18][19] areapplicable to the specified shapes of the peg and hole, while thestrategies with rich information from vision and F/T sensors[13][14] can deal with several type of shapes.
Meanwhile, in industrial applications, hardware based
compliance has been popular for the peg-in-hole methods since
the proposal of the remote center of compliance (RCC)
mechanism by Whitney [20]. With an RCC device, even a
simple controller can provide fine peg-in-hole assembly.
Therefore, an RCC based system is useful in practicalsituations. However, the RCC device is specified to one target
task. Additionally, RCC can only deal with a hole on ahorizontal surface, and the edge of the hole must be planed off.
Yun et al. realized a two-dimensional peg-in-hole method byreinforcement learning with a 3-DOF manipulator with passive
compliance joints [21]; however, there were no realexperimental results. The main drawback of passive
compliance devices like RCC is that the target peg and hole are
specified. This might be the reason why most of the studies
took the software based approach. However, a passive
compliance device has merits. For example, uncertainties ofthe states can be reduced, F/T sensors which are usually highcost are not needed, and a controller for the device can be
simple.
This study challenges a hardware based approach anddevelops a novel passive wrist joint (PWJ) with a pushactivate-rotation (PAR) function. The PAR function involves arotation around a vertical axis automatically activated bypushing the wrist in the vertical direction. This study alsopresents the procedure utilizing the PWJ and the PAR function;a) inclining the peg so that the peg can make frictional contact
with two sides of the hole for the alignment while restoringelastic energy, and b) completing the insertion by activating the
PAR function while utilizing the contact constraint and therestoring force. While different from conventional peg-in-holestrategies which use frictionless contact, our strategy utilizes
frictional contact. It should be noted that frictional contact canbe called jamming, which normally should be avoided in aconventional peg-in-hole assembly. This study rises to thechallenge of effectively utilizing it. The other novel features of
the approach are the following: 1) the passive compliance
Y. Suzuki, T. Tsuji, and T. Watanabe are with the Faculty of MechanicalEngineering, Institute of Science and Engineering, Kanazawa University,
Kakuma-machi, Kanazawa, 9201192 Japan (e-mail: te-watanabe@ieee.org)

absorbs uncertainties of the states of the peg and hole, 2) noactive rotational joints are required for the manipulator part, 3)
F/T sensors are not used; rather, an IMU sensor is used, and 4)
multiple shapes of the peg or hole are available, e.g.,
rectangular, circular, hexagonal, and triangular prisms.
Different from RCC devices, the proposed system can deal
with multiple shapes of chamferless hole or peg and a hole ona horizontal surface.

the peg was completely inserted by pushing the peg indirection. To realize the state shown in Fig. 2, the method forinclining the peg is required, and the proposed strategy (B) is
adopted. Any active rotational joints are then not required in
the manipulator part.

II. PROBLEM DEFINITION AND STRATEGIC OVERVIEW
Aiming at a simple system, this study presents a peg-inhole assembly via an xyz automatic positioning stage shown in
Fig. 1(a). Note that the system can work at normal 6 DOF
manipulators if adopting the same strategy. The developed
passive wrist joint and the gripper were attached to the tip ofthe xyz automatic positioning stage. The state and shape of thehole are given, and the edges of the hole were not planed off.
A camera was utilized to identify the (initial) state of thegrasped peg, but the estimation error was considered as part of
the uncertainty of the state. The procedure (Fig. 1(b)) started
with picking a peg, capturing the bottom face of the peg by thecamera to estimate its state, and inserting the peg into the hole.
The coordinates in this study were defined as shown in Fig.
1(a) where the origin was located at the geometrical center ofthe hole, the axis corresponds to the normal direction of thehole or the table including the hole, and the axis corresponds
to the depth direction. The longitudinal direction of the peg was
assumed to coincide with axis at the initial state. An IMU(acceleration) sensor was attached to the gripper so that thepose of the peg/wrist could be estimated irrespective of thepassive motion of the PWJ. Let( ∈ , , ) be therotation angle of the peg around the -th axis. Without loss ofgenerality, it is assumed that when the peg is inserted the hole,
the rotation angle of the peg is (0) and theposition of the peg is(0 ). It is also
supposed that the initial position of the PWJ is at the right side(0) where, ,denotes the position of the
PWJ. Letbe the initialand0 was assumed
0, the rightconsidering the symmetry of the system. If
and left sides of the procedure only should be inverted. We will
present the strategy where the posture angle between the axis
and the longitudinal direction of the peg is only required to bemeasured, under the assumption that the hole is known.
For convenience, we will explain the case when the shapeof the bottom face of the hole and peg is a quadrangle. The key
objectives for the peg-in-hole method are as follows:(A) To bring the peg into the state shown in Fig. 2.
(B) To utilize frictional contact to incline the peg bytranslational motion.
At the state in Fig. 2, we have static frictional contacts at
the left and front sides of the hole, and restored elastic energy
in – and – directions. If we push the peg/PWJ in the –direction in this state, the PAR function is activated and therotation around the axis, which can generate a large torque,occurs. The large torque causes the static frictional contacts tobecome kinetic frictional contacts, and the peg rotates whilst
keeping the contact with the two sides of the hole. Owing to
the contact constraint and passive compliance of the PWJ, thebottom face of the peg was totally inserted into the hole. Then,(a) Peg-in-hole system(b) Peg-in-hole procedure
Figure 1. Peg-in-hole system and its procedure

Figure 2. Key state of the peg (orange color) and hole (gray color) forcompleting the peg-in-hole

III. PASSIVE WRIST JOINT (PWJ) WITH PAR FUNCTION
A. Design requirements
To realize the presented strategy, the following design
requirements for the PWJ were considered.
1.

Positive rotation around the axis is activated by apushing motion in the
direction (PAR function).

2.

Passive compliance is embedded in the , , anddirections. Note that0 to facilitate the peg-in-holeon a vertical wall.

Fig. 3 shows the structure of the developed PWJ, which was
mainly constructed from a rotational shaft (in red) and a shaft
bearing (light blue). The shaft bearing enables rotation aroundaxis. As shown in Fig. 4, the turned-up gears are attached on
the rotational shaft in a circular manner. Springs bent by thewires are attached on the bearing so that the springs can contact
the turned-up gears. When there is no external force, the PWJ
freely rotates around the axis. If the compression force (forexample, due to the contact with a table) is applied to the PWJ
in thedirection, the rotational shaft translates to contact
with the springs, and the springs are likewise compressed.
Because the springs are bent, the bending proceeds and the gear
teeth are pushed, which causes the positive rotational motion
around the axis. By utilizing stiff springs, the rotation aroundtheaxis can generate a large torque. This
structure/mechanism is referred to as the Push-ActivateRotation function (PAR function). If the compression force isreleased, the springs go to the next space of in gear teeth andthe PWJ irreversibly rotates a constant amount around theaxis. Owing to this function, the rotation can be generated
without any actuators by mere contact with the table.
The shaft bearing includes a partly silicone structure (Fig.
3). Owing to the silicon parts, the PWJ rotates when the peg iscaught in the hole, or the translational motion is prevented bycontact friction, as shown in Fig. 5. The silicone parts wereattached so that the PWJ can rotate around theaxis (Fig.
5(a)) while the PWJ can only positively rotate around axis;
0 (Fig. 5(b)) to facilitate a peg-in-hole on a vertical wall.

(a) Passive compliance in the rotation around the y-axis.

(b) Passive compliance in the rotation around the x-axis.
Figure 5. Passive compliance of the developed wrist joint.

B. Feasible study
In order to confirm the functionality of the PWJ, theexperiments shown in Fig. 6 were conducted. The gripper
holding a peg attached on the PWJ attached on the xyz
automatic positioning stage was utilized.

Figure 3. Schematic of the structure of the developed wrist joint.
are the dimension of the wrist.

Figure 4. Schematics of the mechanism of PAR function, , andLet∈
be the output of the acceleration sensor in∈be the output at time . In thethe initial state andproposed strategy, the direction for inclining the peg can be
specified, and consequently, the posture angle between theprovideaxis and the longitudinal direction of the peg
enough information to solve for the incline. By utilizing the
IMU information, , and , is given by:
∙
cos
(1)
| || |In the experiment shown in Fig. 6(a), we examined theposture angle of the PWJ when applying a load at the tip of
the peg with a force gauge (IMADA DS2-50N). Fig. 7 shows
the results when the loading direction were theanddirections. Note that the results when loading in the
direction can be regarded as the same as those in the
direction owing to the symmetry of the structure. Fig. 7 showsthat the posture changed little when loading in the
direction
while the posture substantially changed when loading in theother directions. The results revealed that the peg can be
inclined by the translational motion of the PWJ, and the PWJ
has the constraint of0.
In the experiment shown in Fig. 6(b), we confirmed the
PAR functionality of the PWJ. We examined the angle of therotation generated by the PAR function when pushing a tablewith the peg. The mean angle was 28° (σ 1.9 when thenumber of the tests was 5. Next, we examined the torquegenerated by the rotation. The peg shown in Fig. 6(b) was
utilized. The force at the action point was measured by theforce gauge when activating the PAR function. Fig.8 shows aresult for the relation between the pushing distance in the
direction and the torque activated by PAR function. It can beseen that when the pushing distance is within 8, 0 , a passive
compliance can be obtained by compressing the PWJ while the
PAR function is not activated. The mean torque was 0.50 Nm(
3.0 10when the number of the tests was 5. Then,the peg can be inserted into the hole by the activated rotationalmotion which can generate a large torque, even when there is apostural error around the axis.

Figure 9. Schematic view of the system setup in this study.
(a) System setup for measurement of(b) System setup forthe adaptability.
measurement of the torque.
Figure 6. System setups for feasible study.

Figure 7. Load applied by the force gauge versus the posture angle

B. Procedure
Based on the proposed strategy given in Section II, we werechallenged to produce the procedure including the following
features as procedure requirements:.

1.

The same procedure is applicable to different shapes ofpegs and holes.

2.

F/T sensors are not needed, with only
given at (1)derived from IMU sensory information needed.

3.

Postural error around the axis is removed by the PARfunction.

4.

Positioning and postural errors are allowed.

For convenience, the procedure for a rectangular prism ispresented as a representative procedure (Fig. 10). Here, thepoint of the peg that is first inserted into the hole is referred toas the First-Insertion point (FI point). At the initial state, thelowest point of the bottom face of the peg in the direction is
selected as the FI point. If there are multiple lowest points, thelowest point in the direction is selected as the FI point.
Step 1) Move the PWJ to the initial position, ,(How to determine theis described in
the next subsection).

Figure 8. Pushing distance indirection versus torque activated by PAR
function

IV. PROCEDURE FOR PEG-IN-HOLE
A. System for Peg-in-Hole
For convenience, the table was constructed from atransparent acrylic and the camera was set to observe the peg
on the table. The posture of the peg around the axis (on thex-y plane) was estimated by the camera image (See Fig. 9).

Figure 10.

Step 2) Move the PWJ downward in the
direction such that0 , which is determined so that a passive
compliance can be obtained by compressing the PWJ
while the PAR function is not activated. After that, wemove it in the
direction with an increment of
0 (see the next subsection for the definition of ). Then,the contact between the peg and the table becomes a line
contact.
Step 3) Move the PWJ in the
direction with a constant
speed of . The peg tilts and the FI point is inserted into

Schematics of the peg-in-hole procedure and time series data of the posture angle

the hole or becomes a point-contact point. In both cases,
the contact friction prevents the translational motion. If
the lateral force due to the input for the lateral motion isgreater than the frictional force, the peg starts sliding on
the table. If the FI point goes into the region of the hole(the hatching area in Fig. 10), the peg is caught by thehole. After that, the peg moves in the caught state, andthenincreases. Whenreaches the threshold,we judge that contact with the edge of the hole has
occurred and stop the motion. The contact point isreferred to as First-Contact point (FC point) (red point in
Fig. 11). The edges of the peg and hole including the FC
point are respectively referred to as FCp and FCh edges.
The operation is for the insertion of the FI point and thealignment between the FCp and FCh edges (at the leftside edge of the hole). The energy is restored at the PWJ.
It is noted that the position of the FC point on the FCp andFCh edges change with the subsequent operations.
Step 4) Move the PWJ in the
direction with a constant
speed of . Owing to the release of the restored energy at
the PWJ, the inclination of the peg decreases, and the peg
becomes close to a standing-up posture. We stop the
motion whenreaches the threshold. By thisoperation, the vertex of the peg, whose y-coordinate value
is the lowest, is inserted into the hole.
Step 5) Move the PWJ in the
direction with a constant
speed of . Similar to Step 3, the peg first inclines andthen slides. If the peg is caught by the edge of the hole,increases. When reaches the threshold, we judge
that contact with the (front) edge of the hole has occurred,and consequently stop the motion. The contact point isreferred to as the second-contact point (SC point) (bluepoint in Fig. 11). The edges of the peg and hole including
the SC point are respectively referred to as SCp and SChedges. The alignment between the SCp and SCh edges isrealized (at the front side edge of the hole). The energy is
restored at the PWJ.
Step 6) Move the PWJ in the
direction with a constant
speed of . Owing to the release of the restored energy at
the PWJ, the inclination of the peg decreases, and the peg
becomes close to a standing-up posture. We stop the
motion whenreaches the threshold. The state
shown in Fig. 2 is then realized.
Step 7) Move the PWJ downward in the
direction. The peg
rotates around the axis owing to the PAR functionality.
The rotation around the axis is constrained by the FChand SCh edges, and the bottom face of the peg iscompletely inserted into the hole. From this state, the peg
is completely inserted into the hole by pushing the peg inthe – direction.

Figure 11.
Schematic view of the peg (orange color) and hole (graycolor), when the orientation of the peg does not correspond to that of the holeat the initial state;
0 (Case II).

Here, the method to tune
is presented.
andare thresholds for detecting a contact with the edge of the hole.
The values should be large enough not to incorrectly detect
stick-slip, but to accurately detect the contact. We measured
the values at the tests three times and tuned the values.
andare the thresholds for getting the peg back to standing-up
posture. The requirement for the tuning is to keep the contacts
at the FC and SC points, which have been obtained in theprevious steps. Here, we show the determination method for.
can be turned similarly to. Fig. 12 shows thewhen moving the PWJ in thetime-series data of
direction with a constant speed of
3 mm/s) in Step 4,
although we did not stop the motion with a threshold. The peg
stood up when ≅ 1.5°. After that, the contact at the FC point
was lost and the contact point moved from the left to the rightside. We conducted the same tests three times and found thewhere the contact at the FC point is not always lost while
the peg is close to the standing-up posture as much as possible.
It is remarked that as it can be seen, each step needs not threedimensional postural information of the peg but only , andthen the acceleration sensor is only required.
The operation at Step 6 has a risk of preventing the insertionand converge at
0, namely jamming, but this is always
avoided. Proof is shown in the appendix.

Figure 12. Time-series data of the posture angle when moving the PWJ
in the + direction with constant speed (3 mm/s) at Step 4, although we did
not stop the motion with a threshold.

C. Determination of the initial position
The initial position must be set so that FI point of the peg
can be inserted into the hole in Step 3. In Step 2, the peg is
inclined by the translation in the
direction. Therefore, at thesliding motion in the
direction in Step 3, the peg also slides
0 be the maximum
in thedirection (Fig. 13). Letamount of the sliding, which was practically examined in
multiple experiments. Let,
be the range offor the area of the hole. Then, the coordinate value of theinitial point should be in the interval,.
Expressing the area of the hole by , we define the area :
,

|

∈

,

∈

,

is the hole area where the FI point should be positioned at
Step 1, considering the sliding in the
direction in Step 3.
The bottom face of the peg is supposed to be captured by
the camera. Let
capturedimage,(bottombe the FI point at theface).
Let,,
be the position of the PWJ when
capturing the image for the bottom face of the peg. Then, we
set the initial point
as follows (Fig. 14):,,,denotes the geometric center ofwherethe area . By this setting, we maximize the possibility of thesuccess of the first insertion of the FI point.

Figure 13.

Sliding in thefor each peg/hole number. The peg-in-hole tasks weresuccessful for all numbers except for No. 7. When trying No.
7, the FI point was not inserted at Step 3 because of a small
inclination of the peg, and thus, the operation failed. Fig. 16
shows the time-series data of the posture angle at No.1.
12

3

Number (No.)
4
5

6

7

8

Quadrangle
HexagonCircleTringle10×20
20×30
Figure 15. Pegs used in the experiment and their initial states when0
The shape and orientation of the hole corresponds to each number of the peg.

direction when the PWJ moves in the –direction(a) State captured by the camera(b) Initial position of the peg
Figure 14. Selection of the initial position of the peg (orange color)

V. EXPERIMENTAL VALIDATIONS
To evaluate the presented PWJ and procedure (strategy),
several experimental tests were conducted. The parameters
used in the experiments were as follows:
7 mm, z
20 mm,
3 mm/s,3.5°,
3 mm, z1.4°,
4.5°, and
1.4°. The clearance of the hole
was set to be 0.1 mm.
A. Peg-in-hole without postural error around the
direction
We conducted the peg-in-hole tests when the initial posture0°).
of the peg coincided with the posture of the hole (The shapes and initial states of the bottom face of the target
pegs are shown in Fig. 15. There were five types of shape, andthe tests were conducted with eight patterns of the peg/holeorientation because different orientations of quadrangular andtriangular peg/hole can have different results. All peg/holes
were chamferless. The tests were started from the state where
the peg was picked. The initial position was determined by themethod given in Section IV.C, and the procedure described in
Section IV was performed. The tests were conducted 3 times

Figure 16. Time-series data of the posture angle
for No.1 peg.

with the procedure

B. Peg-in-hole with initial postural uncertainties aroundthe z axis
Here, we conducted peg-in-hole experiments where theinitial orientation of the peg did not correspond to theorientation of the hole (0). The target pegs were No.1, 2,
3, 4, and 6 in Fig. 15. The experimental procedure was asfollows: 1) The peg was randomly placed on the table. 2) The
orientation angle of the peg | | was measured by the camera.
3) The initial position
for the PWJ was determined by themethod given in Section IV.C. 4) The procedure for the pegin-hole operation was performed. The results were investigatedby splitting the range of | | (0– 50°) into incremental ranges
each spanning 5° ( 0– 5, 5– 10, ⋯ ). We repeated theexaminations until the number of trial times for each range wasover three. Fig. 17 shows the success rate. It can be seen that if
the angle | | was under 30°, the success rate was 100%,
except for No. 2. The (absolute) rotational angle activated by
the PAR function is 28° on average (see section III.B), and it ishard to compensate | | 28 °. Note that the angle of 28 °depends on the tooth interval of the gear as well as the stiffnessof the springs. Note also that when the rotational angle is morethan 28°, compression release of the PWJ is required.

Therefore, if the angle | | was over 30°, the success rate
drastically decreased. In the case of No. 2, the vertex of the peg
was not inserted at Step 4. This was also true for No. 6. Instead,
SC point was obtained at the end of Step 4. The difference
depends on whether different FC and SC points can be obtainedat the end of Step 5. Different FC and SC points were obtainedfor No. 6 while they were not for No.2 because the length
between FC and SC points at the end of Step 4 was large forNo.6 and small for No. 2 (see Fig. 18). The length decreased
during the translation in Step 5. Step 5 has a role in stopping
the sliding and achieving static frictional contact. For No. 2,
FC and SC points became one contact point, and the peg was
not constrained as expected. Hence, the subsequent procedures
failed. Meanwhile, for No. 6, the contact points did not unify,
and the constraints of the peg were as expected at the end of
Step 5. Therefore, the subsequent procedures worked well.

operation range of the PWJ. The gripper picked the peg at,, 0 , which indicates there could be apositional error when picking the peg. The experiments wereconducted with the initial orientation angles (| |) of 0, 15 and
45° for each position of the peg. The tasks succeeded for all
positions and angles. Fig. 20 shows the example where the,and the initial orientation
peg’s position wasangle (| |) was 45°. If the initial angle was over 28°, then the
PAR functionality was activated by releasing the compression
force after the activation. After that, the presented procedure
was performed to complete the insertion.

Figure 19. Control schema for peg-in-hole in real situation

Figure 17. Initial orientation angle (| |) measured by the vision
sensor versus the success rate of the peg-in-hole operation.

(a) No.2(b) No.6
Figure 18. The length between FC and SC points at Step 5

C. Procedure for real-world situation
In this section, we present the procedure for a real-world
situation where a randomly located peg is picked and inserted
into the hole. When the initial posture angle for the picked peg| | is under 28°, the procedure described in Section IV isadapted. When the angle | | is over 28°, the PARfunctionality was activated and the compression was releasedso that | | can be under 28° before continuing. After that, theprocedure for the peg-in-hole operation was performed. Fig.19
illustrates a summary of the control schema for a peg-in-hole
operation in an uncertain environment. The experiment in thissection evaluated the usefulness of the control schema and therobustness to uncertainties caused by vision processing andpicking. The No. 1 peg was used in this test. First, the peg wasplaced in a position sufficiently distant from the hole shown in
Fig. 20. To evaluate the robustness for position uncertainty, theexperiments was conducted with 5 different positions of
peg;
,
,
,
1 mm and,2 mm , where,

was randomly selected from the

Figure 20. Peg-in-hole assembly in a real-world situation for the No. 1 peg
45° and the initial position was randomly selected.
when

D. Verification of procedure requirements
The first experiment showed that the presented procedurecan be applied to different shapes of the peg and hole, although
the procedure did not work for the peg No. 7 (a limitation).
Even for different shapes of the peg and hole, Steps 1–5
provided the alignments at the left and front edges of the hole,and brought the peg into the state shown in Fig. 2. Therefore,
the presented procedure worked for the different shapes of thepeg. In other words, the presented approach is valid for shape
uncertainties. Requirements 2 and 3 were obviously satisfied.
Requirement 4 was validated by the third experiment. In all,we concluded that the passive compliance and the PARfunction provided the realization of the assembly under state
uncertainties. Additionally, the assembly with the clearance of
0.1 mm was realized. Lastly, the unilateral passive complianceof the PWJ facilities a peg-in-hole on a vertical wall. Pleaserefer to our video-clip for an actual test result. We adopted thesame strategy with the same parameters as the one given at theprevious subsection.
VI. CONCLUSION
This study developed a novel passive wrist joint with PushActivate-Rotation (PAR) function for a peg-in-hole operation
with state uncertainties for the peg. A novel strategy utilizing apassive joint and PAR functionality was also proposed for the
peg-in-hole. No active rotational joints were required for the
manipulator part for realization. We did not utilize force/torquesensors; instead, an IMU sensor was used to estimate the initial
posture of the peg during the assembly. The archived clearanceof the hole was 0.1 mm. With the same procedure, we
succeeded in realizing different shaped pegs with rectangular,
circular, hexagonal, and triangular bottoms. The validity of the
proposed wrist joint and strategy was validated by several
experiments. The increased rate of the assembly process andthe further investigation of the potential of the developed
passive wrist joint will be included in our future work.
APPENDIX
Fig. 21 shows the low-dimensionalized model for the
analysis at Step 6. Here we can assume:(2)
where is force applied by the compressed PWJ, is spring
constant of the PWJ and is the compression quantity of the
PWJ. When the peg is translated in the
direction, two cases
can occur: either the right contact point shown in Fig. 21 slides,
or it does not slide. In the former case, the peg is inserted. In
the latter case, d is increased by the translation, and then isalso increased to overcome maximum static frictional force.
This causes sliding at the contact point. Therefore, the insertion
proceeds without jamming at Step 6. It should be noted thateven when the bottom contacts with the right corner andjamming occurs, the inclination of the peg can decrease owing
to the compression of PWJ.

Figure 21. Schematic view for jamming analysis in Step 6.

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